SOLUTION: The length of a right triangle is 14 centimeters shorter than the other leg, and the hypotenuse is 2 centimeters longer then the longer leg. Find the lengths of all three sides.

Question 827416: The length of a right triangle is 14 centimeters shorter than the other leg, and the hypotenuse is 2 centimeters longer then the longer leg. Find the lengths of all three sides.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = long leg
y = short leg
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y = x - 14
h = x + 2
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h = sqrt( xx + yy )
hh = xx + yy
(x + 2)(x + 2) = xx + (x - 14)(x - 14)
xx + 4x + 4 = xx + xx - 28x + 196
xx - 32x + 192 = 0
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the above quadratic equation is in standard form, with a=1, b=-32, and c=192
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -32 192
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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x = 24
x = 8
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h = sqrt( 24*24 + 8*8 )
h = 25.298221281347036
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answer:
x = long leg = 24 cm
y = short leg = 8 cm
h = hypotenuse = 25.2 cm
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