SOLUTION: the length of a rectangular frame is 9 cm more than the width. the area inside the frame is 90 square cm. find the width of the frame. set up a quadratic equation to solve it.

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Question 568677: the length of a rectangular frame is 9 cm more than the width. the area inside the frame is 90 square cm. find the width of the frame. set up a quadratic equation to solve it. THANKS in advance
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width be x cm.
The length (in cm) is x%2B9.
The area of the rectangle is length time width. In square centimeters, it's
x%28x%2B9%29=x%5E2%2B9x
If that is 90 square centimeters,
x%5E2%2B9x=90
The expected quadratic equation answer is probably highlight%28x%5E2%2B9x-90=0%29, although x%5E2%2B9x=90 and x%28x%2B9%29=90 are equivalent equations.
To solve it, you could factor, complete the square, or use the quadratic formula.
Factoring, we see that x%5E2%2B9x-90=%28x%2B15%29%28x-6%29 so the equation transforms into
%28x%2B15%29%28x-6%29=0 with solutions x=6 and x=-15.
Since the width of a frame is measured as a positive number, the only solution to the problem is
highlight%28x=6%29.
The width of the frame is 6 cm. The length is 15 cm (6%2B9=15).