A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width

P = Perimeter = 2 (length) + 2 (width). Let the width be x; then if the length is 5 times longer than the width, the length is 5x.

Plug these values into the Perimeter equation P = 2 (length) + 2 (width):

P = 2 (5x) + 2 (x), or P = 12x, and this is known to have the value 192 units. Solve for the width, x:

(192 units) = 12x gives us x = 16 units. Then the length is 5 (16 units) = 80 units.

Check: Does 2 (80 units) + 2 (16 units) = 192 units? If so, then our width (16) and length (80) are correct.