Question 816341: A rectangle is drawn so the width is 71 inches longer than the height. If the rectangle's diagonal measurement is 85 inches, find the height.
Give your answer rounded to 1 decimal place.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! w = h + 71
d = 85 = sqrt( ww + hh )
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85 = sqrt( ww + hh )
85^2 = ww + hh
85^2 = (h + 71)(h + 71) + hh
85^2 = hh + 142h + 71^2 + hh
2h^2 + 142h + 71^2 - 85^2 = 0
2h^2 + 142h - 2184 = 0
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the above quadratic equation is in standard form, with a=2, b=142, and c=-2184
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to solve the quadratic equation, plug this:
2 142 -2184
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
h = 13
h = -84
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the negative root doesn't make sense for a length, so use the positive root
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Answer:
h = 13 in
w = 84 in
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