A rectangle has perimeter 70 km, and its area is 286 sq-km. Find the dimensions of this rectangle. (For purposes of this problem only, the width is shorter than the length.)

Answer 1

286 =LW

70 = 2(L+W)

L+W =35

L=35-W

(35-W)W = 286

-W^2 +35W -286 =0

W^2 -35W + 286 = 0

use the quadratic formula unless you happen to notice it can be factored as (W-22)(W-13)

W = 35/2 + or - (1/2)sqr(1225-4(286))= 35/2 + or = 9/2

W = 22 or 13

22x13 = 286

L= 22 km long

W = 13 km wide