Question

The length of a rectangular garden is 8 feet longer than its width. The garden's perimeter is 180 feet. Find the length of the garden.

Answer 1

The perimeter of a rectangle is given by the formula below

$P=2l+2w$

Furthermore, we know that the length is 8 feet longer than the width; this is

$\begin{gathered} l=w+8 \\ \text{and} \\ P=180 \end{gathered}$

Therefore,

$\begin{gathered} \Rightarrow180=2l+2w \\ \Rightarrow180=2(l+w) \\ \Rightarrow90=l+w \\ \Rightarrow90=(w+8)+w \\ \Rightarrow2w=82 \\ \Rightarrow w=41 \end{gathered}$

The width is equal to 41 ft; thus,

$\begin{gathered} \Rightarrow l=41+8=49 \\ \Rightarrow l=49 \end{gathered}$

Therefore, the length of the garden is equal to 49 ft.