Question

The length of rectangular sign is 12 less than twice the width. Its perimeter is 114 ft. Find the length and the width of the sign.

Answer 1

The sum of length and width of a rectangle is half the perimeter. Here the sum of length and width is 114/2 = 57 ft.

If we add 12 ft to this total, we have a value that is 3 times the width.

The width of the sign is 69 ft/3 = 23 ft.

The length of the sign is (2·23 -12) = 34 ft.

_____

From the problem statement, using L and W for length and width:

... L = 2W -12

... P = 114 = 2(L +W)

Dividing the second equation by 2 and substituting for L, we have ...

... 57 = (2W -12) +W

... 69 = 3W . . . . . . . . add 12

... 23 = W . . . . . . . . . divide by 3

Answer 2

Answer:

Width=23 Lengh=34