Question

If the sides of a square is increased by 3cm, the area becomes 64 cm^2. How do you find the length of a side of the original square?

Answer 1

The original size was `5 cm`

Explanation:

Let `a` be the original side of the square.

We know that if the side is increased by `3` the area of the new square is `64 cm^2`. So we can write that:

1. `a >=0` because `a` is a geometrical dimension and they are never negative.
2. The area of square with 3 cm longer sides is `64 cm^2`, so we can write `(a+3)^2=64`

Since we are only looking for positive values of `a` (because of pt. 1) we can take a square root of both sides of the equation to get: `a+3=8`.
Now after substracting `3` from both sides we get the answer: `a=5`