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.
|
|
|
