If two opposite sides of a square are increased by 14 meters and the other sides are decreased by 8 ..

Question

If two opposite sides of a square are increased by 14 meters and the other sides are decreased by 8 meters, the area of the rectangle that is formed is 75 square meters. Find the area of the original square.

Answer 1

How I would go about solving this question is I would list the the factors of 75:

1, 3, 5, 15, 25, and 75.

We can find the area of the new rectangle using 2 of these numbers. They just have to multiply to 75

I am going to pick 15 and 5.

We now have a rectangle whose width is 15 and length is 5. To get to the old square, we can set up 2 equations. Mine would look something like this.

(Length = L, Width = W)

L + 14 = 15

W - 8 = 5

Now, just solve for the Length and the Width!

L = 1, W = 13

The area of this rectangle is 13.

While we got the right area, we need to find the area of a square, and the shape we just made wasn't a square because the length and width are different.

Lets choose different numbers; 25 and 3.

L + 14 = 25

W - 8 = 3

L = 11, W = 11

Looks like we found our answer!

L x W = area......11 x 11 = 121

Hope this helps!