Answer:
Step-by-step 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.
<h3>Setup</h3>
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)
<h3>Solution</h3>
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.
