SOLUTION: Is it possible for a leg of a right triangle to be longer than its hypotenuse? If it is, when does this occur? IF it is not, why not?

Question 178014: Is it possible for a leg of a right triangle to be longer than its hypotenuse? If it is, when does this occur? IF it is not, why not?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Is it possible for a leg of a right triangle to be longer than its hypotenuse? If it is, when does this occur? IF it is not, why not?
-------------------
Impossible.
Assume leg b is greater than hypotenuse c.
-------------------
Pythagoras says c^2 = a^2 + b^2
Therefore a^2 = c^2 - b^2
--------
But if b > c then b^2 > c^2, and a^2 would be negative.
If a is a Real Number a^2 cannot be negative.
Therefore both a < c and b < c
================================
Cheers,
Stan H.
RELATED QUESTIONS
Solve the given problems. The area of a right triangle is 168 square meters Find... (answered by ikleyn)

The length of one leg of a right triangle is 24 ft. The length of the other leg is 16... (answered by funmath)

Will someone show me the steps to solve this problems so that I will be able to work... (answered by Earlsdon,funmath)

Is it possible to solve for the other two sides of a right triangle if the Hypotenuse is... (answered by Edwin McCravy)

This is my math question but im not sure how to solve it. One leg of a right triangle is... (answered by KMST)

I need help on this problem. i know this is classic for some of you but not for me.... (answered by richwmiller)

A right triangle has one leg two centimeters longer than the other. The hypotenuse is 17... (answered by checkley77)

1. the larger leg of a right triangle is 3cm longer than its smaller leg. The hypotenuse... (answered by LinnW)