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


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

Please answer quickly!

Find the equation of the line.

Y=__x + __



y = 3x + 3

Step-by-step explanation:

Using slope intercept form: y = mx + b

where m is the slope(rise over run/change in y over change in x), and b is the y intercept(point where x is 0). We can derive the equation by simply using our mathmatical principles of slope and y intercept. Because our y intercept is where x is 0. Our y intercept is 3 since x is 0 when y is 3 because it touches the axis. Since y is 6 when x is one.

y = mx + b

6 = m(1) + 3

-3 -3


3 = m


m = 3


An m of 3 means that you rise 3 every 1 run or 3y every 1x.

Therefore, our equation in slope intercept is:

y = 3x + 3

Sales tax is calculated as a percentage of the sales price. If sales tax is 7%, what is the sales tax on clothing that costs $150?




Step-by-step explanation:

You multiply $150 by .15 to find out what 15% of it  (10.50)

You add the values to get $160.50

10.5 is  the sales tax on clothing that costs $150

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given that Sales tax is calculated as a percentage of the sales price.

sales tax is 7%

We need to find the the sales tax on clothing that costs $150

Convert 7% to the decimal value by dividing with 100.


Now multiply 0.07 with 150


Zero point zero seven times of one hundred and fifty.


Hence, 10.5 is  the sales tax on clothing that costs $150

To learn more on Percentage click:



What is the solution of the equation x2=64


The answer for the equation is x=32

Please help me solve this problem!! I WILL GIVE YOU BRAINLIEST!
(Algebra 1)




Step-by-step explanation:

Move the variable to the left,


Collect like terms so you would have,


Then divide and switch the sign because you divided,


Use the Distributive Property to simplify 17(2b + 3)​


the answer is 34b + 51



Step-by-step explanation:

When you distribute, you multiply the number on the outside of the parentheses by everything inside of the parentheses. So...



Because you can't tell what x is, this is the most simplifying you can do.

Hopefully this helped you out...have an amazing day :3

From 9:00 p.m. to 6:00 a.m., the temperature dropped 1.6 degrees Fahrenheit per hour.

What was the total change in temperature, in degrees Fahrenheit, between 9:00 p.m. and 6:00 a.m.?


Answer: help plz

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

The original price of a play ticket was $36.00. Yolanda bought the ticket at original price and then marked it up 10% and resold the ticket. How
much did she resell the ticket for?


she sold the ticket for $39.50
explanation: you take 36 and time it by 10% and it will give you $3.60 and you add it to 36

In the image above, what do the red arrows on lines mean?


Answer: ............................Step-by-step explanation:You need to attach an image

Evaluate 3{5 + 3[10 + 4.8]}​




Step-by-step explanation:




1. 30

2. 0.83333333

3. 1.2

4. 30

Step-by-step explanation:

H is the only reasinable decimal

Solve proportion 2/4.5=t/0.5


0.2 or 2/9 in fraction form I believe.

Which inequality matches the graph shown?



I am pretty sure it is x>8 which is B.

Step-by-step explanation:

I’m one hundred percent positive it’s B because if it’s open the aren’t less then or equivalent to or greater than or equivalent to

The length of a rectangle is 11 less than 9 times the width. The perimeter of the rectangle is 18 inches


Length = 7   Width = 2

Step-by-step explanation:

L = Length

W = Width



2(9W-11) + 2W = 18

18W - 22 +2W = 18

20W -22 = 18

20W = 40

W = 2

L = 9(2)-11



you are listening to a playlist that has three hip hop songs 2 rock songs if they are a 15 more songs on this playlist and the ratio of hip hop song or rock song stayed the same how many of each type would be on this playlist ​


doing this fa points , sorry not sorry .

Steven sells bags of different kinds of cookies. He made $27 selling bags of Oreos, $18 selling chocolate chips cookies, and $45 selling chunky sugar cookies. Each bag of cookies costs the same amount. What is the most that Steven could charge for each bag of cookies?



9 dollars

Step-by-step explanation:

It would be 9 dollars because that is the only common factor that could go into 27, 28, or 45.

what is the answer for −3x−6+(−1)


Hi it would be -9x-1 hope that helps



Step-by-step explanation:

Combine like terms

-6+-1 = -6-1 = -7

Hence, it's -3x-7

Joe and Carmen are partners in a business. Joe makes $2.00 profit for every $5.00 profit that Carmen makes. If Carmen makes $20 on the first item they sell, how much profit will Joe make?


Joe will make a $8.00 profit

people wont solve my question i need it ASAP



A pig has 10,000 kg mass more than a mass

Step-by-step explanation:


When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, start text, space, m, L, end text of chocolate syrup for every 333 ounces of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, start text, space, m, L, end text of chocolate syrup for every 666 ounces of hot water. Which hot cocoa is more chocolatey? Choose 1 answer: Choose 1 answer:



45mL hot cocoa is more chocolatey

Step-by-step explanation:

When Arjun makes hot cocoa, if he add 20mL of chocolate syrup to 3ounces of water, let us know the equivalent chocolate in one ounces of water.

20mL = 3 ounces

x = 1 ounce

cross multiply

3x = 20

x = 20/3

x = 6.67 mL

This means he must have add 6.67mL of chocolate to 1 ounce of water.

Similarly, if 45mL is added to every 6 ounces

45mL = 6ounces

x = 1 ounce

cross multiply

6x = 45

x = 45/6

x =  7.5mL

This means he must have add 7.5mL of chocolate to 1 ounce of water.

The hot cocoa that is more chocolatey is the one with the highest amount of chocolate in 1 ounce. That is 45mL hot cocoa


eli's cocoa is more chocolately. i would show proof (on khan academy), but I just skipped the q. :|

Step-by-step explanation:

Write 2.08 x 10^2 in standard form.​




Step-by-step explanation:

If you multiply 2.08 by ten to the second power (100) Then you get 208

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  The given expression can be written in the standard form as 208.

What are Scientific notations?

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

The given expression can be written in the form of an expression as shown below.

2.08 x 10²

= 2.08 × 100

= 208

Hence, the given expression can be written in the standard form as 208.

Learn more about Scientific notation here:



Convert y = x2 - 4x + 1 to vertex form by completing the square.

O y= (- 1)2 + 4
O y= (1 - 2)2 +5
O y= (x - 2)2 – 3
O y = (x - 4) + 1



vertex: (-2, -3)

Step-by-step explanation:

y = x2 + 4x                 + 1  

y = x2 + 4x + 22          + 1 - 22  

y = (x + 2)2 + 1 - 4  

y = (x + 2)2 - 3            in y = (x - h)2 + k, (h, k) is the vertex.  



y = (x - 2)² - 3

Step-by-step explanation:


y = x² - 4x + 1

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 1

   = (x - 2)² - 3





Step by step

determine the defined range

remove parentheses

move the terms

collect like terms and calculate

divide both sides

A survey asks students to name their favorite outdoor activity. 12 students say bike riding, 8 students say climbing trees, and 5 students say swimming. Mia says that 40% olf the students say their favorite activity is climbing trees. Is she correct? Explain



Mia is incorrect. 32% of the students say climbing trees is their favorite.

Step-by-step explanation:

Percentage of the students that chose climbing trees = number of students that chose climbing trees ÷ total number of students surveyed × 100

Number of students that chose climbing trees = 8

Total number of students = those that chose riding bike + those that chose climbing trees + those that say swimming = 12 + 8 + 5 = 25


% of the students that say climbing trees = [tex] {8}{25}*100 = \frac{800}{25} = 32 [/tex].

Mia is wrong.

32% say climbing trees is their favorite. NOT 40%.


Using the exponential notion and simplify pls


Evaluate or simplify?
It would be 8000 I think. I’m sorry if it’s wrong!

If someone could help me I would really appreciate it!

Factor by slide and divide!




Step-by-step explanation:

6x^2 + 7x + 24

= 6x^2 + (15-8)x + 24

= 6x^2 + 15x - 8x + 24

= 3x( 2x+5 ) - 4( 2x+5 )

= (3x-4)(2x+5)

Write an equation or inequality to represent the relationship "three
times a number decreased by 12 is equal to -18". Then solve.
a. Equation :
b. Answer:



a. 3x-12= -18 b. x=-2

Step-by-step explanation:

simplify the expression (5x^7)^2




Step-by-step explanation:

Measure the angle and classify it as right, acute, or obtuse.




Step-by-step explanation:

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Combine like terms to simplify the expression. 5 x + 4 + 2 x + 5



[tex] \huge{ \boxed{ \bold{ \text{7x + 9}}}}[/tex]

Step-by-step explanation:

[tex] \text{5x + 4 + 2x + 5}[/tex]

[tex] \text{Combine \: like \: terms} : [/tex]

[tex] \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}[/tex]

[tex] ➝ \: \text{5x + 2x + 4 + 5}[/tex]

➝ [tex] \text{ 7x + 4 + 5}[/tex]

[tex] \text{Add \: the \: numbers : 4 \: and \: 5}[/tex]

[tex] ➝ \: \text{7x + 9}[/tex]

[tex] \text{Hope \: I \: helped}[/tex]!

[tex] \text{Best \: regards}[/tex]!

~[tex] \mathfrak{TheAnimeGirl}[/tex]


7x + 9

Step-by-step explanation:

Combine like terms, means put the ones that have something in common together; in this case they are the terms with an 'x' value, and a regular numeric value.

5x+2x = 7x

5+4 = 9



value of 3b^2 - 5c^3 if b = 2 and c = -1​




Step-by-step explanation:

3(2)^2 - 5(-1)^3

3(4) - 5(-1)

12 + 5


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