SOLUTION: One leg of a triangle is 14 meters longer than the other leg. Thy hypotenuse is 26 meters long. Find the length of each leg. 26=14n+n This is the equation I came up with.

Algebra ->  Equations -> SOLUTION: One leg of a triangle is 14 meters longer than the other leg. Thy hypotenuse is 26 meters long. Find the length of each leg. 26=14n+n This is the equation I came up with.       Log On


   

Question 200270: One leg of a triangle is 14 meters longer than the other leg. Thy hypotenuse is 26 meters long. Find the length of each leg.
26=14n+n This is the equation I came up with.
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
square root of
x^2+(x+14)^2=26^2
square root of a^2+b^2=c^2

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
Let the shorter leg be s, then the longer leg is s + 14
Applying the Pythagorean formula, or a%5E2%2Bb%5E2=c%5E2, we get:

s%5E2+%2B+%28s+%2B+14%29%5E2+=+26%5E2

s%5E2+%2B+s%5E2+%2B+28s+%2B+196+=+676

2s%5E2+%2B+28s+-+480+=+0, or 2%28s%5E2+%2B+14s+-+240%29+=+2%280%29

(s + 24)(s – 10) = 0

s = - 24 or 10.

Since a measurement cannot be negative, we reject s = - 24. Therefore, the shorter leg of this triangle, or s, is 10 meters long,
and the longer leg, or (s + 14) is 24 meters long