Why is it that when comparing a squares area with a rectangles area, with the SAME PERIMETER, that the square has a greater area?

Answers

Answer 1

s = side length of square

4s = perimeter of square

L = length of rectangle

W = width of rectangle

P = 2L+2W = perimeter of rectangle

4s = 2L+2W .... since we want the perimeters the same

4s = 2(L+W)

s = 0.5(L+W)

s^2 = (0.5(L+W))^2 ... square both sides

s^2 = 0.25(L+W)^2

The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.

-----------------------------------

The area of the rectangle is LW

Let's subtract this from the area of the square and see what we get

A = area of square = s^2

B = area of rectangle = LW

C = difference in area

C = A - B

C = s^2 - LW

C = 0.25(L+W)^2 - LW

C = 0.25(L^2+2LW+W^2) - LW

C = 0.25L^2+0.5LW+0.25W^2-LW

C = 0.25L^2-0.5LW+0.25W^2

C = 0.25(L^2-2LW+W^2)

C = 0.25(L-W)^2

Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.

So C is always positive as long as [tex]L \ne W[/tex]

If C > 0, and C = A - B, then

C > 0

A-B > 0 .... replace C with A-B

A > B .... add B to both sides

This shows the square area is always larger than the rectangle.

Again this only works if L and W are different values. If L = W, then the argument falls apart because the rectangle becomes the square.

We make [tex]L \ne W[/tex] to have a nonsquare rectangle.


Related Questions

Is this the correct answer? Please someone help!!!

Answers

Answer:

yes

Step-by-step explanation:

same slope

Answer:

yes same slope

Step-by-step explanation:

would u expect the product of 43.5 and 1.0001 to be greater than or less that 1 or equal to 43.5

Answers

Answer:

Greater

Step-by-step explanation:

since it has a 0.0001 and not just 1 its greater 43.5

WILL GIVE BRAINLIEST IF CORRECT

Answers

Answer:

la respuesta correcta es laC

han ku po ammo paumahin

Please help D: what’s the answer

Answers

I think it’s the 6 I’m not sure tho
BBBBBBBBBBBB I TOOK THE TEST

Alex wrote checks on Tuesday for $35 and $40. He also made a deposit in his checking account of $170. Find the overall change in the amount in his checking account.

Answers

Answer: He retrieved 75$ from his account then he put back 170$ so +75 and -170 so in total the answer would be 245$

Answer:  He would have $100 in his bank account from the information provided .

Could someone show me how to do this?

Answers

Step-by-step explanation:

b - no:of students on bus

V - " " on van

so the eqtn is

12v+10b=698

14v+2b=244

so when you solve these two eqtns you get

V=9

b=59

The cost of a speeding ticket is a function of each mile per hour that exceeds the speed limit multiplied by a fixed rate of $2 plus a $40 processing fee.Write the function that represents this relationship.Then determine the cost of a speedingticket for a car that has gone 50 mph in a 35 mph zone

Answers

The cost of the speeding ticket for a car that has gone 50 mph in a 35 mph zone is $70.

Describe Function?

In mathematics, a function is a relationship between two sets of numbers, known as the domain and the range, that assigns each element of the domain a unique element in the range. A function can be thought of as a machine that takes input from the domain and produces output in the range.

More formally, a function f from a set X to a set Y is denoted as f: X → Y

For example, the function f(x) = 2x assigns to each real number x a unique real number 2x. When x = 1, f(1) = 2; when x = -3, f(-3) = -6.

Functions can be represented in a variety of ways, including algebraic expressions, tables of values, and graphs. The graph of a function is a visual representation of the relationship between the input and output values, and can be used to analyze the behavior of the function.

Functions are important in many areas of mathematics, science, and engineering, and are used to model relationships between quantities, solve problems, and make predictions. They are also used in computer programming, where they are used to encapsulate behavior and modularize code.

The function that represents the relationship between the speed of a car and the cost of a speeding ticket can be expressed as:

C(x) = 2(x - L) + 40

where:

C(x) is the cost of the speeding ticket for a car traveling at speed x (in mph).

L is the speed limit (in mph).

(x - L) represents the number of miles per hour over the speed limit that the car was traveling.

The fixed rate is $2 per mile per hour over the limit, and there is a $40 processing fee added to every ticket.

To determine the cost of a speeding ticket for a car that has gone 50 mph in a 35 mph zone, we substitute the values for x and L into the formula above:

C(50) = 2(50 - 35) + 40

C(50) = 2(15) + 40

C(50) = 30 + 40

C(50) = $70

Therefore, the cost of the speeding ticket for a car that has gone 50 mph in a 35 mph zone is $70.

To know more about number visit:

https://brainly.com/question/29766862

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What do I need to put down for these?

Answers

3x-4 hope this helped

3x + 5.9 = 14.6
What's the answer?

Answers

Answer: X=2.9

Step-by-step explanation:

Find m 1 if m 2=47.6

Answers

Answer:

try 130.4, I got my answer by subtracting 47.6 with 180. How'd I get 180? the angles are obtuse so that means it'll add up to 180. Thus the answer is 130.4

in a neighborhood the ratio of houses with swing sets to houses without swing sets is 3 to 5. if the number with swing sets is 270 how many houses do not have swing sets

Answers

Answer:

450? why did I get that?

Step-by-step explanation:

The number of houses not having swing sets is 450.

Given that, in a neighbourhood, the ratio of houses with swing sets to houses without swing sets is 3 to 5 and the number with swing sets is 270.

We need to find out how many houses do not have swing sets.

What is the ratio?

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

Let the number of houses that do not have swing sets be x.

So that the proportion is 3/5 = 270/x

⇒3x=270×5

⇒x=450

Therefore, the number of houses not having swing sets is 450.

To learn more about the ratio visit:

https://brainly.com/question/13419413.

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What transformation keeps proportinality

Answers

There are four main types of transformations; translation, rotation, reflections, and dilation.

The cost to manufacture x number of chairs can be represented by the function C(x)=36x. In this context, what does the statement C(63)=2268 mean?

Answers

Answer:

The cost to manufacture 63 chairs, and that cost is 2268.

Step-by-step explanation:

Mathematical Models

The cost to manufacture x chairs is given as the math model:

C(x)=36x

For example, to manufacture 10 chairs, we write:

C(10)=36*10=360

According to the explained above, the statement C(63)=2268 means we are calculating the cost to manufacture 63 chairs, and that cost is 2268.

As an estimation we are told 5 miles is 8 km.
Convert 27.5 miles to km.

Answers

Answer:

44 km

Step-by-step explanation:

8/5 is the conversion between m and km which is 1.6 and then we can simply multiply 27.5 times 1.6 which is 44 km I hope this helps.

i will give brain QUICK please

how much will fill in 1 second

Answers

Answer:

I'd say 1/2 a gallon

Step-by-step explanation:

What is the value of 7×7+23

Answers

Answer:

72

Step-by-step explanation:

7x7 = 49

49 + 23 = 72

PEMDAS causes the multiplication to come before the addition.

−8 1/4+3 1/4

The "1/4" counts as a fraction. :)

Please help!!

Answers

i believe the answer is -5

The price of Stock A at 9 A.M. Was ​$14.67. Since​ then, the price has been increasing at the rate of ​$0.08 each hour. At noon the price of Stock B was ​$15.17. It begins to decrease at the rate of ​$0.15 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Price of Stock A at 12 : 00 A.M. is :

A = 14.67 + 0.08×3

A =  $14.91

Price of Stock B at 12 : 00 A.M. is :

B = $15.17

Let, after x hours price are same :

[tex]14.91 + 0.08x = 15.17 -0.15x\\\\0.23x = 15.17-14.91\\\\0.23x =0.26\\\\x = 1.13\ hours[/tex]

At, 1 : 13 P.M both stocks have same prices.

Hence, this is the required solution.

help please i'll love you forever thanksssss . *btw i am going to post a lot of questions if you answer & explain I'll give you brainliest each time .*

Isabella noticed that when she doesn't study for a test, on average she makes a 45. Isabella also realizes that for every hour she studies, on average she scores an additional 7 points. Which of the following represents g, get average test score she studied for h hours?

a. 7-5h=g
b. 7+5h=g
c. 45+7h=g
d. 45-7h=g

Answers

Answer:

C. 45 + 7h = g

Step-by-step explanation:

This one would be correct because you have to add 7 points to the 45 points she would get on average without studying, without forgetting to multiply 7 by the number of hours that Isabella studied.

Example:

Let's say that Isabella studied for 3 hours. We could replace the h for the number of hours that she studied.

45 + 7(3) = g

Now you just have to solve the equation.

45 + 21 = g

Following the rules of PEMDAS, you would get rid of the parenthesis first by multiplying 7 times 3. Now you just have to add and you will have your answer for g.

g = 66

can someone please help me with this question

Answers

Answer:

60 in^3

Step-by-step explanation:

You just multiply the base by the height.

Answer:600

Step-by-step explanation: hope this helps you

If 72 is 9 times larger than 8, which statement below is true?
A) 8 is 72 times larger than 9
B) 72 is 8 times larger than 9
C) 9 is 8 times larger than 72
D) 8 is 9 times larger than 72

Answers

B - because 72 is 9 times larger than 8. Therefore, 72 is also 8 times larger than 9. You can flip multiplication around just like addition.

a number multiplied by 5 and increased by 7 the result is 62

Answers

Answer:11

Step-by-step explanation: subtract 7 from 62, which give you 55, divide by 5 which gives you 11.

Answer:

Step-by-step explanation:

5X+7=62

5X=55

X=11

 

The distance required to stop a car varies
directly as the square of its speed. If 250
feet are required to stop a car traveling 60
miles per hour, how many feet are required to
stop a car traveling 96 miles per hour?

Answers

Answer:

400

Step-by-step explanation:

what times is equal to 75​

Answers

Answer: 5 x 15= 75

Step-by-step explanation:

Answer:

75*1=75

Step-by-step explanation:

Function h(x) = x + 4
If your input was 2, what is your output?

Answers

Answer:

h(2)=6

Step-by-step explanation:

just plug in 2 where you have an x, and you’d have 2 + 6, which equals 6

is 9/36 greater than 8/1

Answers

Answer:

No it's not

Step-by-step explanation:

The reason is because 8/1 becomes a whole number unlike the other.

Name a pair of acute vertical angles

Answers

Heres a answer for your question

ok, this is the last question I need help with(I think) please answer. I give Brainliest for best answer

Answers

Answer:

D) 132.67 (this seems to be the closest to the answer, I hope it helps)

Step-by-step explanation:

First, have the area of circle formula: A = π r²

Then, you need to find the radius to be able to complete the area formula. So, since you have the circumference, you will need to use it to find the radius:

C = 2 π r

40.82 = 2 π r

20.41 = π r

r = 6.496704777 . . . Do not round! Rounding will not give an exact answer!

Now that you have the radius, plug in:

A = π r²

   = π (6.49 . . .)²

   = π  (42.20717296 . . .) Do not round! Rounding will not be exact!

   = 132.5977445 . . .

   ≈ 132.6

Which one?
A. B. C. or D? ​

Answers

Answer: 1,176

Step-by-step explanation:  -3 times -7 is positive 21.

21 times -8 is negative -168

-168 times -8 is positive 1,176

It’s cccccccccccccccccc

Mr. Garcia wants to leave a 15% tip to his server at Applebee's. If his total was $75, how much would his total be including the tip? *

$11.25
$90.00
$86.25
$75.15

Answers

A 11.25
Anything else is to much
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