Question

Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of some traffic sign must be 96 inches. Also, its length is 10 inches longer than its width. Find the dimensions of this sign.

The width of the sign is:

The length of the sign is:

Answer 1

You have a length and a width. Let's call them L and W.

We know that the length is 10 inches longer than the width, which means that
L = W + 10.

Next, we know the perimeter is 96 inches. We are going to assume that the shape of the sign is rectangular. The perimeter of a rectangle is L + W + L + W, or
96 = 2W + 2L

Let's rewrite these two equations nearer to each other:
L = W + 10
96 = 2W + 2L

We know what L is equal to (W+10), so we are going to substitute W + 10 everywhere we see an L in the second equation. This gives us
96 = 2W + 2(W+10)

Solve for W, which will in turn let you solve for L.