SOLUTION: One leg of a right triangle is 2 inches smaller than the hypotenuse. The other leg is 5 inches long. What are the lengths of the unknown leg and hypotenuse?

Question 91066: One leg of a right triangle is 2 inches smaller than the hypotenuse. The other leg is 5 inches long. What are the lengths of the unknown leg and hypotenuse?
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
One leg of a right triangle is 2 inches smaller than the hypotenuse. The other leg is 5 inches long. What are the lengths of the unknown leg and hypotenuse?
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Use the Pythagorean theorem to solve this. The Pythagorean theorem states:

Where a and b are the legs, and c is the hypotenuse. Let a be the leg that is 5 inches long. You can write an expression for the other leg (b) in terms of the hypotenuse:

Now, you have 2 equations and 2 unknowns. Substitute this expression for b and the given value for a into the Pythagorean theorem:

Now solve for c:
First, square the binomial:

Subtract c^2 from each side of the equation:

Solve for c:

To find b, substitute this value for c back into the given expression for b:

Good Luck,
tutor_paul@yahoo.com

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