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.

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

Width=23 Lengh=34

57 732

step-by-step explanation:

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