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.

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) (Show Source): You can put this solution on YOUR website!
Using the Pythagorean theorem: where c (the hypotenuse) = 26, we can write:
1) and...
2) "The sum of the legs...is 34 meters." Rewrite this as:
and substitute into equation 1).
1a) Simplify and solve for b.
1b)
1c) Rearrange into the standard form for a quadratic equation.
1d) Divide by 2 to ease the calculation a bit.
1e) Factor this trinomial.
1f) so...
or
So the two legs are:
a = 24 and b = 10 (or vice versa if you like)
Check:

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