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?

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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) About Me  (Show Source):
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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:
a%5E2%2Bb%5E2=c%5E2
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:
b=c-2
Now, you have 2 equations and 2 unknowns. Substitute this expression for b and the given value for a into the Pythagorean theorem:
5%5E2%2B%28c-2%29%5E2=c%5E2
Now solve for c:
First, square the binomial:
25%2Bc%5E2-4c%2B4=c%5E2
Subtract c^2 from each side of the equation:
25-4c%2B4=0
Solve for c:
29-4c=0
-4c=-29
highlight%28c=29%2F4%29
To find b, substitute this value for c back into the given expression for b:
b=29%2F4-2
highlight%28b=21%2F4%29
Good Luck,
tutor_paul@yahoo.com