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

Answer:

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

Step-by-step 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 $0.64(0.91463414634)=0.58536585365\approx 0.59$.