An oriental rug is 3 feet longer than it is wide. if the diagonal of the rug is 12 feet, find its dimensions to the nearest tenth of a foot.

L = W + 3

L^2 + W^2 = 12^2

Substituting for L:-

(W + 3) ^2 + W^2 = 144

2W^2 + 6W + 9 - 144 = 0

2W^2 + 6W - 135 = 0

W = [-6 + / 1 sqrt (6^2 - 4*2*-135) ] / 2*2

W = 6.85

so L = 9.85

Answer to nearest tenth = length 9.9 ft, width 6.9 ft.