If the sides of a square are decreased by 2 cm, the area is decreased by?

Question

If the sides of a square are decreased by 2 cm, the area is decreased by
36 cm2. What were the dimensions of the original square?
show the work so I can learn it please. I am so confused

Answer 1

The area of a rectangle is the length (call it "x") times the width (call it "y"). Because it is a square, however, length is equal to width (so x=y), so instead of "area = x times y" we can say "area = x times x, or x^2". We know that the area of the ORIGINAL square is x^2. We also know that in the new square, each side is reduced by 2, so our equation for the new square is (x-2)^2. Finally, we know that the difference between the areas of the two squares is 36, so we can put this all together to make the equation:
x^2 - (x-2)^2 = 36

use your FOIL rule on the second part, and you get
x^2 - x^2 + 4x - 4 = 36

the two different "x^2"s will cancel each other out, so we get
4x - 4 = 36
so we get

4x = 40
divide by four, and we get

x = 10
so we know that each side of the original square is 10!

and that's how you do it!

Answer 2

You can find the relationship by making an equaiton:

1- lets take X to be the original side of a square so that X^2 is the area of that original square.

2- lets take X-2 to be the new dimensions, so that the area of the new sqaure is (X-2)^2.

3- Therefore, the difference in the area between both squares will give you the difference:

X^2 - (X-2)^2 = D (Difference in area)

4- If you expand this and simplify you will end up with 4X - 4 = D

Lets take the example where the original size X = 10 cm.

therefore if you replace X by 10, you will get:

4(10) - 4 = 36 as

40 - 4 = 36

Using this equation, you can do the reverse. If the difference in area is 36, you replace D with 36 and work out X:

4X - 4 = 36

threrfore, take the -4 to the other side:

4X = 40

and now you want to solve X, so you divide both sides of the equation by 4 :

X = 10

Hope that helps.

Answer 3

let x = length of one side of the square (before it is decreased)

The area of a square with side x is x^2, or x squared. Since the side is being decreased by 2, the left side should be x-2, so the new area on the left side of the equation is (x-2)^2. Since this decreases the area by 36, the right side of the equation is x^2 (the original area) minus 36 (the amount that the area decreased by).

Once you get the first line, the rest is just solving for x, and you get 10.

(x-2)^2 = x^2-36
x^2-4x+4 = x^2-36
-4x+4 = -36
-4x = -40
x = 10

Answer 4

The relationship of a side of a square to the area is a:a^2

For example, if a side is 3 untis long, than the area is 9 units^2

Then, if the length of a side is decrease by 2, then the length
is a-2. Thus, the area is decreaesd by (a-2)^2

Since the area decreased by 36 cm, solve for 'a':

(a-2)^2 = a^2-4a+4 = 36 -----------> a^2-4a-32=0

Factor, you get (a-8)(a+4), since 'a' can't be negative, a=8

Since 'a' = original length decreased by 2, then the length of the original square = 10

Answer 5

Let the side of the original square be l.
The side of the smaller square will be l-2
Then,
l*l – (l-2)*(l-2) = 36
(l + (l-2))*(l-(l-2)) = 36
(2l -2)*(2) = 36
4*(l -1) = 36
(l – 1) = 9
l = 10
Verfy : 10*10 - 8*8 = 100 - 64 = 36.

Answer 6

original square was 10 cm
10x10=100
10-2=8
8x8=64
100-64=36
i did this through trial and error. good luck