# 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?

Oct 6, 2015

The original size was $5 c m$

#### 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 $64 c {m}^{2}$. So we can write that:

1. $a \ge 0$ because $a$ is a geometrical dimension and they are never negative.
2. The area of square with 3 cm longer sides is $64 c {m}^{2}$, so we can write ${\left(a + 3\right)}^{2} = 64$

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: $a = 5$