Question

Find the dimensions of the rectangle

Answer 1

• length: 12 m
• width: 4.5 m

Explanation:

The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.

Setup

Let w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.

A = LW

54 = (2w +3)(w)

Solution

Rewriting this equation to standard form gives ...

2w² +3w -54 = 0

(2w -9)(w +6) = 0 . . . . factored

w = 9/2, -6 . . . . . . . . . values that make the equation true

Only the positive width makes sense in a geometry problem, so we have ...

w = 9/2

length = 2w +3 = 12

The length of the rectangle is 12 meters; its width is 4.5 meters.