SOLUTION: The hypotenuse of a right triangle is 5m long. The longer leg is 1m longer than the shorter leg. Find the side lengths of the triangle. Find the length of the shorter side Fin

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a right triangle is 5m long. The longer leg is 1m longer than the shorter leg. Find the side lengths of the triangle. Find the length of the shorter side Fin      Log On


   

Question 1088561: The hypotenuse of a right triangle is 5m long. The longer leg is 1m longer than the shorter leg. Find the side lengths of the triangle.
Find the length of the shorter side
Find the length of the longer side
Find the length of the hypotenuse
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let the hypotenuse be c, the longer leg a, and the shorter leg b
if the hypotenuse of a right triangle is 5m long, we have
c=5m
if the longer leg is 1m longer than the shorter leg, we have
a=b%2B1m
since we have a right triangle, than
c%5E2=a%5E2%2Bb%5E2.....plug in c=5m and a=b%2B1m
%285m%29%5E2=%28b%2B1m%29%5E2%2Bb%5E2......solve for b
25m%5E2=b%5E2%2B2b%2Am%2B1m%5E2%2Bb%5E2
25m%5E2=2b%5E2%2B2b%2Am%2B1m%5E2
2b%5E2%2B2b%2Am%2B1m%5E2-25m%5E2=0
2b%5E2%2B2b%2Am-24m%5E2=0...divide by 2
b%5E2%2Bb%2Am-12m%5E2=0...factor
b%5E2-3b%2Am%2B4bm-12m%5E2=0
%28b%5E2-3b%2Am%29%2B%284bm-12m%5E2%29=0
b%28b-3m%29%2B4m%28b-3m%29=0
%28b+-+3m%29%28b+%2B+4m%29+=+0
solutions:
%28b+-+3m%29=+0=>b=3m
since triangle side, we don't need negative solution
so, a=b%2B1m=>a=4m


the length of the shorter side:3m
the length of the longer side:4m
the length of the hypotenuse:already given, 5m


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The hypotenuse of a right triangle is 5m long. The longer leg is 1m longer than the shorter leg. Find the side lengths of the triangle.
Find the length of the shorter side
Find the length of the longer side
Find the length of the hypotenuse
Classical 3-4-5 Pythag. triple, so since hypotenuse is 5 m, the shorter and longer legs must be 3 m and 4 m, respectively.

Why is the length of the hypotenuse being sought? Isn't that given as part of the problem?