Question

The perimeter of a rectangle is 37. The length is 1 less than 12 times the width. What is the length and width of the rectangle ?

Answer 1

Width = W
Length = 12W - 1
Perimeter = 2L + 2W = 37

In the perimeter equation substitute the length equation in for L to get the equation in terms of W
2L + 2W = 37
2(12W - 1) + 2w = 37

Distribute
2(12W - 1) + 2w = 37
24W - 2 + 2w = 37
26W = 39
W = 3/2 = 1.5
Width = 1.5

Lastly, solve for length
L = 12W - 1
L = (12 • 1.5) - 1
L = 18 - 1
L = 17
Length = 17