SOLUTION: The area of aright triangle is 84 square ft.; its hypotenuse is 25ft. Find the length of its two sides.

Question 930841: The area of aright triangle is 84 square ft.; its hypotenuse is 25ft. Find the length of its two sides.

Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The area of aright triangle is 84 square ft.; its hypotenuse is 25ft. Find the length of its two sides.
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a*b/2 = 84
a^2 + b^2 = 25^2
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Can you do the rest?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we have two equations here
x^2 + y^2 = 25^2
(xy)/2 = 84
the two equations become
x^2 + y^2 = 625
xy = 168
solve second equation for y and substitute in first equation
x^2 + (168/x)^2 = 625
x^2 + (28224/x^2) = 625x^2
x^4 + 28224 = 625x^2
x^4 -625^2 + 28224 = 0
solve using quadratic formula and we get two sets of solutions
x^2 = 49, which means x = 7 feet and y = 24 feet
x^2 = 576, which means x = 24 feet and y = 7 feet

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