Chapter 12.6, Problem 7P

To determine

To find: the side of original square.

Answer to Problem 7P

The side of Original Square will be $7cm$ .

Explanation of Solution

Given information:

The area of new square is $100c{m}^2$ and the side of the new square is increased by $\left(a+3\right)cm$ .

Formula:

The area of square is $a^2$ where $a$ is any side length of square.

Calculation:

Consider the side of Original Square be $a$ .

As mentioned above the side length is increased by $3cm$ .

Therefore the new side of a square is $\left(a+3\right)$ then the area of square is $100c{m}^2$ .

Therefore the area of square is

  $\begin{array}{l}100={\left(a+3\right)}^2\Rightarrow 100=a^2+6a-91\Rightarrow a^2+13a-7a-91=0\\ \Rightarrow a\left(a+13\right)-7\left(a+13\right)=0\Rightarrow a=7,-13.\end{array}$ .

We will consider the side as $7cm$ because side cannot be negative.

Therefore the side of Original Square will be $7cm$ .