SOLUTION: A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet

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Question 1078427: A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet
Found 2 solutions by MathLover1, jorel1380:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet
let's a hypotenuse be c, one leg a, and other leg b
if a hypotenuse that is 3 feet longer than one leg, we know that c=a%2B3
and, if the other leg is 4 feet, we know that b=4
use Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2.....substitute c=a%2B3 and b=4
%28a%2B3%29%5E2=a%5E2%2B4%5E2....solve for a
a%5E2%2B6a%2B9=a%5E2%2B4%5E2
a%5E2%2B6a%2B9-a%5E2=16
6a=16-9
6a=7
a=7%2F6

then c=a%2B3=>c=7%2F6%2B18%2F6=>c=25%2F6

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the unknown leg. Then:
(n+3)²=n²+4²
n²+6n+9=n²+16
6n=7
n=7/6 feet. ☺☺☺☺