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?

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
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