Question

Area of a patio If each side of a square patio is increased by $4$feet, the area of the patio would be $196$square feet. Solve the equation ${(s+4)}^2=196$ for$s$ to find the length of a side of the patio.

Short answer

The length of a side of the patio is$10$ feet.

Step-by-step solution

Step 1. Given information

Equation${(s+4)}^2=196$

Step 2. Solving equation

$$\begin{gathered} {(s+4)}^2=196 \\ {s}^2+16+8s=196 \\ {s}^2+8s+16-196=0 \\ {s}^2+8s-180=0 \\ {s}^2+18s-10s-180=0 \\ s(s+18)-10(s+18)=0 \\ (s+18)(s-10)=0 \end{gathered}$$

Step 3. Finding solution

As, $(s+18)(s-10)=0$

So, $$\begin{gathered} s+18=0 \\ s=-18 \end{gathered}$$ and $$\begin{gathered} s-10=0 \\ s=10 \end{gathered}$$

As, length cannot be negative. So, the length of a side of the patio is $10$feet.