Question 817647: If a rectangle has an area of 100 square inches and a perimeter of 50 inches, what are its dimensions?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! Lw = 100
L = 100/w
2L + 2w = 50
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2L + 2w = 50
2(100/w) + 2w = 50
200/w + 2w = 50
200w/w + 2ww = 50w
2w^2 - 50w + 200 = 0
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the above quadratic equation is in standard form, with a=2, b=-50, and c=200
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to solve the quadratic equation, plug this:
2 -50 200
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
w = 5
w = 20
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both roots will solve the problem, but traditionally width < length, so choose w = 5.
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Answer:
w = 5 in
L = 20 in
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