SOLUTION: The hypotenuse of a right triangle is 2 units longer than the longer leg which is 14 units longer than the shorter leg. Determine the lengths of the three sides. How do i begin s

Question 246102: The hypotenuse of a right triangle is 2 units longer than the longer leg which is 14 units longer than the shorter leg. Determine the lengths of the three sides. How do i begin solving this question?
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is 2 units longer than the longer leg which is 14 units longer than the shorter leg. Determine the lengths of the three sides. How do I begin solving this question?
What is the formula for the hypotenuse?
a^2+b^2=c^2 where c is the hypotenuse and a and b are the legs

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The Pythagorean Theorem is fundamental to the solution:
, where
c = hypotenuse
a = longer leg
b = other leg
.
The problem setup gives you 3 important relationships.

and

.
So,

.
Of course,

.
Going back to the Pythagorean Theorem:

.
By substitution, we can cast the entire problem in terms of b, the shorter leg.

.

.
Subtract b^2 from both sides

.
Subtract 32b from both sides

.
Subtract 256 from both sides

so,

.
Can we factor 60 such that the factors are 4 apart? 2*30? no 3*20? no. 4*15? no. 5*12? no. 6*10? yes!

.
Thus we have two candidate values for b: 10 and -6. Since the leg of a triangle cannot be negative, the proposed solution is b = 10.
.
Substituting back into what we were told in the problem setup:

.
We always check our proposed solution. Here we just use the Pythagorean Theorem again.

That checks, so we have the correct answer.
Done.
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