The length of a rug is 3 inches less than 8 times the width. The perimeter is 174 inches. Find the length of the rug

Start with determining the length's equation, which is (L = 8w-3). Then, set up the equation for the perimeter which is length + length + width + width = 174, also know as 2w + 2L = 174

Then, plug in your L = equation into the perimeter equation then solve.

2w + 2 (8w - 3) = 174

This equation equals 10, so 10 is your width. Then, plug ten into your L = equation to find your length. The length turns out to be 77