Question

The area of a rectangle is 120 cm2. The length of the rectangle is eight less than the twice of the width. Find the dimensions of the rectangle.

Answer 1

length = 12 cm; width = 10 cm

Explanation:

Let the width = x.

Let the length = y.

xy = 120

y = 2x - 8

Substitute 2x - 8 for y in the first equation.

x(2x - 8) = 120

2x² - 8x - 120 = 0

Divide both sides by 2.

x² - 4x - 60 = 0

Factor the trinomial.

(x - 10)(x + 6) = 0

x - 10 = 0 or x + 6 = 0

x = 10 or x = -6

Since x is the width, it cannot be a negative number, s discard the solution x = -6.

width = x = 10

length = 2x - 8 = 2(10) - 8 = 20 - 8 = 12

Answer: length = 12 cm; width = 10 cm