SOLUTION: The sum of the lengths of the two legs of a right triangle is 34 meters. If the length of the hypotenuse is 26 meters, find the length of each leg.

Algebra ->  Triangles -> SOLUTION: The sum of the lengths of the two legs of a right triangle is 34 meters. If the length of the hypotenuse is 26 meters, find the length of each leg.      Log On


   

Question 210724This question is from textbook College Algebra
: The sum of the lengths of the two legs of a right triangle is 34 meters. If the length of the hypotenuse is 26 meters, find the length of each leg. This question is from textbook College Algebra

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Using the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 where c (the hypotenuse) = 26, we can write:
1) 26%5E2+=+a%5E2%2Bb%5E2 and...
2) a%2Bb+=+34 "The sum of the legs...is 34 meters." Rewrite this as:
a+=+34-b and substitute into equation 1).
1a) 26%5E2+=+%2834-b%29%5E2%2Bb%5E2 Simplify and solve for b.
1b) 676+=+%281156-68b%2Bb%5E2%29%2Bb%5E2
1c) 676+=+1156-68b%2B2b%5E2 Rearrange into the standard form for a quadratic equation.
1d) 2b%5E2-68b%2B480+=+0 Divide by 2 to ease the calculation a bit.
1e) b%5E2-34b%2B240+=+0 Factor this trinomial.
1f) %28b-24%29%28b-10%29+=+0 so...
b+=+24 or b+=+10
So the two legs are:
a = 24 and b = 10 (or vice versa if you like)
Check:
26%5E2+=+24%5E2%2B10%5E2
676+=+576%2B100
676+=+676