Question

The cost $C$ (in dollars) of making a square window with a side length of $ninches$is represented by$C=\frac{n^2}{5}+175$. A window costs $\$355$. What is the side length (in feet) of the window? Justify your answer.

Answer 1

Step: Find the side length $n$ (in feet) of the window that costs $\$355$.

We have given that, the cost $C$ (in dollars) of making a square window with a side length of $ninches$is represented by$C=\frac{n^2}{5}+175$.

Substitute $C=\$355$in the given relation.

$$\begin{gathered} C=\frac{n^2}{5}+175 \\ \Rightarrow 355=\frac{n^2}{5}+175 \\ \Rightarrow 180=\frac{n^2}{5} \\ \Rightarrow 900=n^2 \\ \Rightarrow \sqrt{900}=n\mathbf{(}\mathbf{Take}\mathbf{}\mathbf{the}\mathbf{}\mathbf{positive}\mathbf{}\mathbf{square}\mathbf{}\mathbf{root}\mathbf{}\mathbf{of}\mathbf{}\mathbf{each}\mathbf{}\mathbf{side}\mathbf{)} \\ \Rightarrow 30=n \\ \therefore n=30in.=\frac{30}{12}ft=2.5ft \end{gathered}$$

Hence, the side length of the window that costs $\$355$ is $2.5ft$.