Triangle SUN has sides with lengths of 5, 6, 7 units. Determine whether this triangle is a right triangle.

Question

Triangle SUN has sides with lengths of 5,6,7 units. Determine whether this triangle is a right triangle 

Answer 1

For triangle SUN to be a right angle triangle the square root of the sum of the squares of the adjacent sides should equal

the hypotenuse, whose length should be larger than any of the sides. Therefore in this problem 7 is the larger length and should be the hypotenuse, and 5 and 6 should be the lengths of the other two sides. Calculating:

 

 

√( 5²+6²) = √(25+36) = √61=7.82 ≠ 7 , Therefore this is not a right angle triangle based on the Pythagorean theorem.

 

 

Answer 2

If the sum of the squares of the 2 legs of a triangle is equal to the square of the triangle's hypotenuse, then the triangle is a right triangle.

 

5² + 6² = 7²

 

If statement is true, then it is a right triangle.  Otherwise, it is not.