Question

The area of a rectangle is 24 square inches. Determine both dimensions if the length is 6 inches less than three times the width

Answer 1

Answer:

width is 4 inches

length is 6 inches

Step-by-step explanation:

the length is 6 inches less than three times the width

l = 3w - 6

a = l * w

a = (3w - 6)w

a = 3w^2 - 6w

area of the rectangle is 24 square inches

3w^2 - 6w = 24

subtract 24 from both sides

3w^2 - 6w - 24 = 0

Divide both sides by 3

w^2  - 2w - 8 = 0

Factor

(w - 4)(w + 2) = 0

w = {-2, 4}

disregard the negative root since measurement must be positive

w = 4

l = 3w - 6

l = 3(4) - 6

l = 6