Question

Questions

answered

A rectangle has an area of 108 square inches. The rectangle's length is 6 inches longer than 4

times its width.

3

What is the rectangle's width?

Write your answer as an integer, a simplified proper or improper fraction, or a simplified

radical expression

Answer 1

Considering the area of the rectangle, it is found that it's width of the rectangle is of 3 inches.

What is the area of a rectangle?

The area of a rectangle of length l and width w is given by:

A = lw.

In this problem, we have that:

A = 108, l = 6 + 4w.

Hence, using the equation for the area:

lw = 108

(6 + 4w)w = 108

4w² + 6w - 108 = 0

2w² + 3w - 54 = 0

Which is a quadratic equation with coefficients a = 2, b = 3 and c = -54, hence:

$\Delta = b^2 - 4ac = (3)^2 - 4(2)(-54) = 441$

$x_1 = \frac{-3 + \sqrt{441}}{6} = 3$

$x_2 = \frac{-3 - \sqrt{441}}{6} = -4$

Width is a positive measure, hence it is of 3 inches.

More can be learned about the area of a rectangle at https://brainly.com/question/10489198