The area of a rectangle is 2r^2 + r – 1. The length is 2r – 1. What simplified expression represents the width?
Mathematics · High School · Thu Feb 04 2021
Answered on
Given the equation:
The area of a rectangle is 2r^2 + r – 1.
The length is 2r – 1.
Determine the width of the rectangle.
Solution:
Formula for the area of the rectangle:
A = lw
Equate the values to the formula for the area of the rectangle
2r^2 + r -1 = (2r - 1)w
Divide both sides by 2r - 1 in order to determine the area of the rectangle.
(2r^2 + r - 1)/(2r - 1) = (2r -1)w/(2r- 1)
Expand 2r^2 + r - 1.
(2r - 1)(r - 1)/(2r - 1) = 2
w = r - 1
Final answer:
w = r - 1