Question

A picture frame (see figure) has a total perimeter of 3 feet. The width of the frame is 0.64 times its length. Find the dimensions of the frame. (Round your answers to two decimal places.)

Answer 1

`\approx 0.59\text{ ft by }0.91\text{ ft}`

Explanation:

Let
`\ell` represent the length of the rectangle. The width can be represented as
`0.64\ell`.

The perimeter of a rectangle with lengths
`l` and
`w` is given by
`p=2l+2w`.

Thus, we have:

`2\ell+2(0.64\ell)=3,\\2\ell +1.28\ell=3,\\3.28\ell=3,\\\ell=0.91463414634\approx 0.91`

The width is then
`0.64(0.91463414634)=0.58536585365\approx 0.59`.