SOLUTION: A triangle has sides with lengths of 5 meters, 11 meters, and 12 meters. Is it a right triangle?

Hi, there--

THE PROBLEM:
A triangle has sides with lengths of 5 meters, 11 meters, and 12 meters. Is it a right triangle?

A SOLUTION:
We use the Pythagorean Theorem and its converse to determine if this triangle is a right triangle.

Together these two theorems show that: "The square of one side of a triangle is equal to the sum of the 
squares of the other two sides, if and only if the triangle is a right triangle."

This is that famous equation  you have probably heard of.

We have a triangle with sides of lengths 5m, 11m, and 12m. If this is a right triangle, then the longest 
must be the hypotenuse (the side labeled c.) The other two sides are the legs (sides labeled a and b.)

We will let 
a = 5m
b = 11m
c = 12m

If this triangle is a right triangle then the sum of the squares of a and b will equal the square of c.

Substitute these values into the Pythagorean Equation.


Now simplify each side of the equation and see if you have a true statement.



We see that the two sides of the equation are not equal, and the equation is FALSE.

The sum of the squares of two sides is not equal to the square of the other sides. Therefore, this triangle 
is NOT a right triangle.

Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com