Question

The sides of the rectangle are in the ratio of 4:7. If its length is 31.5 in., find the width, the perimeter, and the area of this rectangle.

Answer 1

Let
`\ell` the length and
`w` the width. By the ratio of the sides:


`(w)/(\ell)=(4)/(7)\Longrightarrow (w)/(31.5)=(4)/(7)\Longrightarrow w=(4\cdot31.5)/(7)\Longrightarrow \boxed{w=18~in.}`

Now, we'll find the perimeter p. We'll use the formula below:


`p=2(\ell+w)\\\\ p=2(31.5+18)\\\\ p=2\cdot49.5\\\\ \boxed{p=99~in.}`

The area of a rectangle is
`S=w\cdot\ell`. Then:


`S=w\cdot\ell\\\\ S=18\cdot31.5\\\\ \boxed{S=567~in.^2}`