Question

the length of a rectangular picture frame is 5 in more than five times the width. the perimeter is 262 in. find the length and the width

Answer 1

"The length is 5 inches more than five times the width" can be expressed as

`l=5+5w`

The perimeter is 262 inches.

So, we have to use the perimeter formula to find the length and width

`\begin{gathered} P=2(l+w) \\ 262=2(l+w) \\ l+w=131 \end{gathered}`

Then, we combine the equations

`\begin{gathered} l+w=131 \\ 5+5w+w=131 \\ 6w=131-5 \\ w=(126)/(6) \\ w=21 \end{gathered}`

Now, we find the length

`l=5+5w=5+5\cdot21=5+105=110`

Hence, the width is 21 inches and the length is 110 inches.