SOLUTION: a right triangle has an area of 84 square feet and a hypotenuse of 25 feet long what are the lengths of its other two sides?

Question 1774: a right triangle has an area of 84 square feet and a hypotenuse of 25 feet long what are the lengths of its other two sides?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
ok, convoluted approach but i cannot think of a simpler method as of yet...
the triangle has an area formula of where a and b are the 2 unknown lengths.
Also, using Pythagoras,
From the first equation, get a= then substitute this into the Pythagoras equation, to get the equation... .
Treat this as a quadratic, and use the quadratic formula, solving for . This gives 2 solutions: b=24 or b=7 (ignoring the negative solutions, since this is a real-time problem dealing with lengths, which cannot be negative.
These solutions give a to be 7 or 24 respectively, ie the 2 solutions are mirror-images of each other.

cheers
Jon.
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