Solve by factoring

Question

The length of a rectangle is 5 centimeters less than 3 times it's width. It's area is 28 square centimeters. Find the dimensions.

Answer 1

A = length x width

let w = width, l = length = 3w - 5

28 = (3w-5)w

distribute: 28 = 3w² - 5w

subtract 28 from both sides and rearrange equation: 3w²-5w - 28 = 0

factor: (3w + 7)(w-4) = 0

3w + 7 = 0; w - 4 = 0

w = -7/3; w = 4 Since the width can't be a negative value, only w = 4 cm makes sense

l = 3(4) - 5 = 12 - 5 = 7

length = 7 cm, width = 4 cm

Answer 2