Arug 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.