SOLUTION: Hi!! I need help with a problem: The lenght of a rectangle is 7 feet more than its width and the area is 120 square feet. Find the dimensions of the rectangle. I have no clue how

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Question 596724: Hi!! I need help with a problem:
The lenght of a rectangle is 7 feet more than its width and the area is 120 square feet. Find the dimensions of the rectangle. I have no clue how to solve it.
Thank you,
I appreciate your help!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The way you are expected to solve the problem depends on what you have been studying in your class.

USING ALGEBRA (quadratic equations):
Let the width of the rectangle (in feet) be x.
The length (in feet) is x%2B7.
The area is x%28x%2B7%29=120 --> x%5E2%2B7x=120 --> x%5E2%2B7x-120=0
Solving (by factoring or using the quadratic formula), we get
x=8 and x=-15
Since the width must be a positive number, the width is highlight%288%29 feet,
and the length (in feet) is 8%2B7=15

USING FACTORS OF 120 (if studying divisibility and prime factors):
120=2%5E3%2A3%2A5 so it must have %283%2B1%29%281%2B1%29%281%2B1%29=4%2A2%2A2=16 factors, including 1 and 120.
Those factors come in pairs that multiplied equal 120.
We just need to find the pair of factors that differ by 7.
120=1%2A120
120=2%2A60
120=3%2A40
120=4%2A30
120=5%2A24
120=6%2A20
120=8%2A15
So far I have listed 7 pairs of factors (14 factors).
There is one more pair, but
15-8=7, so I do not need to go on.
The rectangle is 8 feet wide by 15 feet long.