If we double the side of a square, its area increases by $147 cm^2$. What is the length of the side of the original square?

1. Problem Description

If we double the side of a square, its area increases by $147 cm^2$. What is the length of the side of the original square?

2. Solution Steps

Let $x$ be the length of the side of the original square. The area of the original square is $x^2$.

If we double the side, the new side length is $2x$. The area of the new square is $(2x)^2 = 4x^2$.

The problem states that the area increases by $147 cm^2$. Therefore, the difference between the new area and the original area is $147$.

$4x^2 - x^2 = 147$

$3x^2 = 147$

$x^2 = \frac{147}{3}$

$x^2 = 49$

$x = \sqrt{49}$

$x = 7$

3. Final Answer

The length of the side of the original square is $7$ cm.