Question

Plywood 1: The length of the plywood is twice its width and the area is 4.5sq ft.

Plywood 2: The length of the plywood is 1.4 less than twice its width and the area is 16sq ft.
Plywood 3: The perimeter of the plywood is 10ft. and its area is 6sq ft.

a. What quadratic equation represents the area of each piece of plywood? Write the equation in terms of the width of the plywood.

Answer 1

Plywood 1:

l = 2w

2w² = 4.5

w² = 2.25

w = 1.5 ft, l = 3 ft

Plywood 2:

l = 2w - 1.4

(2w - 1.4)w = 16

2w² - 1.4w = 16

2w² - 1.4w - 16 = 0

10w² - 7w - 80 = 0

(5w - 16)(2w + 5) = 0

5w - 16 = 0

5w = 16

w = 3.2 ft, l = 5 ft

Plywood 3:

lw = 6

l + w = 5

(5 - w)w = 6

5w - w² = 6

w² - 5w = -6

w² - 5w + 6 = 0

(w - 2)(w - 3) = 0

w = 2 ft, l = 3 ft