SOLUTION: The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the legnths of the legs of the triangle.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the legnths of the legs of the triangle.      Log On


   

Question 5535: The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the legnths of the legs of the triangle.
Found 2 solutions by CharStar, Abbey:
Answer by CharStar(110) About Me  (Show Source):
You can put this solution on YOUR website!
a2 + b2 = c2 is the formula for Pythagorean Theorem
a2 = 14
b = b unsolved
c2= 26
14(2) + b = 26(2)
196 + b(2) = 676
Subtract 196 from 676
b= 480
b= square 21.90

Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2+%2Bb%5E2+=+c%5E2
Let a = shorter leg
Let b = longer leg
let c = hypoteneuse
a is 14 feet shorter than b:
a+14=b
a%5E2+%2Bb%5E2+=+c%5E2
we can substitute a+14 in for our b, and use the hypoteneuse value of 26:
%28a%5E2+%2B%28a%2B14%29%5E2%29+=+26%5E2
%28a%5E2+%2Ba%5E2%2B28a%2B196%29+=+26%5E2
2a%5E2%2B28a%2B196=676
divide both sides by two:
a%5E2+%2B14a%2B98=338
subtract 338 from both sides:
a%5E2%2B14a-240=0
%28a%2B24%29%28a-10%29=0
a=-24 or a=10
we can rule out the -24, because we are talking about a distance, which is always positive:
so the shorter leg = 10 feet
Put this back into the equation:
a+14=b
10+14=24, so the longer leg is 24 feet
and this makes sense because
10^2 + 24^2= 100 +576 = 676
and 26*26 = 676