Question

around the 3 sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is 5 feet longer than 2 times its width. Find the length and width of the patio.

Answer 1

Given

Length =5+2w ......(i)

width =w

The light covers 3 sides which is 45

`\begin{gathered} 2w\text{ + L =45}\ldots\text{.}(i) \\ \text{rewrite as L=45-2w} \\ we\text{ solve equation (i) and (ii) simultaneously} \\ L=5+2w \\ L=45-2w \\ \text{Add }the\text{ equation}s \\ 2l=50 \\ \text{divide both sides by 2} \\ l=25ft \end{gathered}`

To find the width

`\begin{gathered} \text{substitute for w in equation(i)} \\ L=25 \\ L=5+2w \\ 25=\text{ 5+2w} \\ 25-5=2w \\ 20=2w \\ \text{Divide both sides by 2} \\ w=10ft \end{gathered}`