I am not good at word problems... please HELP!?

Question

If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square?

Answer 1

The square used to be 10cmx10cm
If the sides were 10 cm, the area is 100 cm^2
If the sides are 8, the area is 64 cm^2
The difference between these numbers is 36, so the original dimensions were 10x10.

Answer 2

Let x = side of square
Area of a square = square of its sides; thus A = x^2
Your problem states that each side is decreased by 2 cm.
The sides of the new square are x - 2
Your problem states that the new area (x - 2)^2 is (or = ) the old area (x^2) less (or -) 36cm^2
Rewriting this: (x - 2)(x - 2) = x^2 - 36
x^2 - 4x + 4 = x^2 - 36
-4x = -40
x = 10
You can check this by taking the area of a square with side 10. 10^2 = 100
Now decrease the sides by two. Each side is 8. Find the area by multiplying the sides: 8 x 8 = 64
Is 64 = 100 - 36?

Answer 3

Set up the general equation:

The area of the reduced volume can be represented as

2cm*Xcm + 2cm*2cm + 2cm*X cm = 36cm^2

Imagine the two squares, the original and one inscribed, just 2cm smaller in widith and height.

The horizontal 2*X element is a rectangle comprising the 2cm height reduction, X is the width of the inscribed square.

The 2*2cm chunk is the square at the corner. It must be the same width as the 2cm height, hence the product for the area.

The vertical element is another 2*X (width times height) rectangle.

So adding all three elements together, the are must equal 36 cm^2

Simplifying

2X+4+2X = 36
4X +4 =36
4X = 36-4 = 32
X = 32/4 = 8cm!

Answer 4

let the original dimension of the side = x cm

area = x^2

after reduction the side = x - 2

area after decrease = (x-2)^2 = x^2 - 4x + 4

so x^2 - (x^2 - 4x +4) = 36

x^2 - x^2 + 4x - 4 = 36

4x - 4 = 36

divide by 4

x - 1 = 9

x = 9 + 1 = 10 cm

Answer 5

Let x = original length of a side of a square

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

Answer: 10 cm

Proof:
= 10^2 - (10 - 2)^2
= 100 - 8^2
= 100 - 64
= 36

Answer 6

let x be the size of the sq

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

so the original sq is 10 x 10

Answer 7

let the original side=x
so area=x^2

given (x-2)^2=x^2-36

or -4x+4=-36

or 4x=40
or x=10