Question 242335: A rectangle has a length 2 meters less than twice its width. When 5 meters is added to the width, the result is a square with an area of 144 square meters. Find the dimensions of the original rectangle
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangle has a length 2 meters less than twice its width.
When 5 meters is added to the width, the result is a square with an area of 144 square meters.
Find the dimensions of the original rectangle.
:
Let x = the width
It says,"A rectangle has a length 2 meters less than twice its width.", therefore:
L = 2x - 2
:
"When 5 meters is added to the width, the result is a square with an area of 144 square meters."
:
(x + 5)*(2x - 2) = 144
FOIL
2x^2 - 2x + 10x - 10 = 144
:
2x^2 + 8x - 10 - 144 = 0
:
2x^2 + 8x - 154 = -
Simplify, divide by 2
x^2 + 4x - 77 = 0
Factors to
(x + 11)(x - 7) = 0
Positive solution
x = 7 m is the original width
:
Find the dimensions of the original rectangle
:
L = 2(7) - 2 = 12 m is the original length
:
:
Will adding 5 m to the width make a square with 144 sq/m?
7 + 5 = 12, then: 12 * 12 = 144 sq/m
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