SOLUTION: the hypotenuse of a right triangle is 1 inch longer than the longer of the two legs. The shorter leg is 7 inches. Find the length of the hypotenuse

Algebra ->  Pythagorean-theorem -> SOLUTION: the hypotenuse of a right triangle is 1 inch longer than the longer of the two legs. The shorter leg is 7 inches. Find the length of the hypotenuse      Log On


   

Question 1078089: the hypotenuse of a right triangle is 1 inch longer than the longer of the two legs. The shorter leg is 7 inches. Find the length of the hypotenuse
Found 2 solutions by themasterofcircuits, MathTherapy:
Answer by themasterofcircuits(27) About Me  (Show Source):
You can put this solution on YOUR website!
Let b denote the longer leg, a denote the shorter leg, and c denote the hypotenuse

c=b+1 (1)
a=7 (2)
Pythagorean theorem:a^2+b^2=c^2 (3)
We have 3 equations and only 2 unknowns, so let's solve them:
First, let's solve for b by substituting (1) and (2) into (3):
(7)^2+b^2=(b+1)^2
49+b^2=b^2+2b+1
49=2b+1
2b=48
b=24
Now we can plug a=7 and b=24 into (3):
c^2=7^2+24^2
c^2=625
[c=25]
Hence, the hypotenuse is 25 inches.

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

the hypotenuse of a right triangle is 1 inch longer than the longer of the two legs. The shorter leg is 7 inches. Find the length of the hypotenuse
Correct answer: