Question 819773: the hypotenuse of a right angle triangle is 18 cm. if one of the other sides is 4 cm longer than the third side. find the lengths of the other two sides
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! h = sqrt( aa + bb )
a = b + 4
18 = sqrt( (b + 4)(b + 4) + bb )
324 = (b + 4)(b + 4) + bb
324 = bb + 8b + 16 + bb
2bb + 8b - 308 = 0
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the above quadratic equation is in standard form, with a=2, b=8, and c=-308
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to solve the quadratic equation, by using the quadratic formula, plug this:
2 8 -308
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
b = 10.5698051
b = -14.5698051
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the negative root doesn't make sense for a length, so use the positive root
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324 = aa + 10.5698051^2
a = sqrt( 324 - 10.5698051^2 )
a = sqrt( 212.27922 )
a = 14.569805
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answer:
a = 14.569805 cm
b = 10.5698051 cm
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