Question 926741: The perimeter of a rectangle is 30 cm. The area is 36 cm^2. Find the longest dimension of the rectangle.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 2L + 2w = 30
Lw = 36
L = 36/w
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2L + 2w = 30
2(36/w) + 2w = 30
72/w + 2w - 30 = 0
w(72/w + 2w - 30 = 0)
72 + 2ww - 30w = 0
2ww - 30w + 72 = 0
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the above quadratic equation is in standard form, with a=2, b=-30 and c=72
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -30 72
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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w = 3
w = 12
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use the root w = 3 (using either root works fine for this problem):
L = 36/w
L = 36/3
L = 12
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answer:
the longest dimension of the rectangle = 12 cm
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