Question

A rectangle has a lenght that is 9 inches less than twice its width. The area of the rectangle is 180 square inches. What is the width of the rectangle?

Answer 1

The width of the triangle is 18.65 inches

Explanation:

From the question, we have;

Length, L = Width, W - 9

Also the area is given by

L × W = 180

Therefore, we have

(W - 9) × W= 180

W² - 9·W = 180

W² - 9·W - 180 = 0

Factorizing or solving with quadratic formula

`(-b \pm √(b^2 - 4ac) )/(2a)`

a = 1

b = -9 and

c = -180

we get

(W + 9.65)(W-18.65) =0

Therefore W = - 9.65 or 18.65

Therefore, the Width, W = 18.65 and the length = W - 9 = 18.65 - 9 =9.65

The width of the triangle = 18.65 inches.

Answer 2

12 inches

Explanation:

In this question, we are asked to calculate the width of a rectangle having a length 9 inches less than twice it’s width and given the area of the rectangle.

First, we identify that the length is 9 inches less than twice the width

meaning if length is l and width is w; then l = (2w-9) inches

Mathematically the area of the rectangle is l * w ; meaning w * (2w-9)

This has a value equal to 180

w * (2w-9) = 180

opening the bracket;

2w^2 -9w = 180

2w^2 -9w - 180 = 0

solving this quadratic equation;

w = 12 or -7.5

since width cannot be negative, w = 12 inches