Question

If two opposite sides of a square are increased by 15 meters and the other sides are decreased by 13 meters, the area of the rectangle that is formed is 60 square meters. find the area of the original square.

Answer 1

Answer: Shown below

Explanation:

Since it's a square, we will refer to its values as x. Using that, we can make an equation for the rectangle.
(x + 15) * ( x - 13) = 60

We can expand it and simplify so that we get a zero on one side and a polynomial on the other.

(x + 15)(x - 13) - 60 = 0

x² + 2x - 225 = 0

We simplify the binomial so we get two answers for x.

(x - 15)(x + 17) = 0

x = 15 and -17

Now we have two answers. So which one is right? Well, the sides cannot be negative, therefore we must use 15 and not -17.

15² = 225

Our answer is 225