SOLUTION: One leg of a right triangle is 2 in. longer than the other leg. The hypotenuse is 10 in. long. What are the lengths of the legs of the triangle?

Click here to see ALL problems on Geometry Word Problems

Question 97137This question is from textbook Intermediate Algebra
: One leg of a right triangle is 2 in. longer than the other leg. The hypotenuse is 10 in. long. What are the lengths of the legs of the triangle? This question is from textbook Intermediate Algebra

Found 2 solutions by Nate, checkley71:
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
Obviously the pythagorus triple: 6,8,10
One leg = x
Other leg = x + 2
a^2 + b^2 = c^2
x^2 + (x + 2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0
(x - 6)(x + 8) = 0
x = 6 and -8
Other leg: 8 or -6
Obviously we cannot accept negative values ...
6 and 8

Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
A^2+(A+2)^2=10^10
A^2+A^2+4A+4=100
2A^2+4A+4=100
2A^2+4A+4-100=0
2A^2+4A-96=0
2(A^2+2A-48)=0
(A-6)(A+8)=0
A-6=0
A=6 ANSWER FOR THE SMALLER SIDE
6+2=8 FOR THE LONGER SIDE
PROOF
6^2+8^2=10^2
36+64=100
100=100