SOLUTION: The Hypotenuse of a right triangle is 168mm long and the Perimeter is 398mm. Determine the lengths of the two others legs.

Algebra ->  Pythagorean-theorem -> SOLUTION: The Hypotenuse of a right triangle is 168mm long and the Perimeter is 398mm. Determine the lengths of the two others legs.      Log On


   



Question 257354: The Hypotenuse of a right triangle is 168mm long and the Perimeter is 398mm.
Determine the lengths of the two others legs.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Our first equation is
(i) a%5E2+%2B+b%5E2+=+168%5E2
and our second equation is
(ii) a+%2B+b+%2B+168+=+398%7D%7D%0D%0Awhich+is%0D%0A%28iii%29+%7B%7B%7Ba+%2B+b+=+230
solving (iii) for a, we get
(iv) a+=+230+-+b
substituting (iv) into (i) we get
(v) %28230-b%29%5E2+%2B+b%5E2+=+168%5E2
expanding, we get
(vi) 52900+-+460b+%2B+b%5E2+%2B+b%5E2+=+28224
or
(vii) 2b%5E2+-+460b+%2B+24676+=+0
By quadratic, we get
b ~ 144.78
a ~ 85.22