How do you use the Pythagorean Theorem to determine if the following triangle with sides a, b, & c is a right triangle: a=5, b=10, c=15?

1 Answer
Apr 17, 2016

c^2 != a^2 + b^2, therefore, this cannot be a right triangle.

Explanation:

The Pythagorean Theorem applies to right angle triangles, where the sides a and b are those which intersect at right angle. The third side, the hypotenuse, is then c

http://www.johncmccloskey.com/math-topics/the-pythagorean-theorem/

To test whether the given lengths of sides create a right triangle, we need to substitute them into the Pythagorean Theorem - if it works out then it is a right angle triangle:

c^2 = a^2 + b^2

15^2 != 5^2+10^2
225 != 25+100
225 != 125

In reality, if a=5 and b=10 then c would have to be

c^2 = 125
c =sqrt(125) = 5sqrt(5)~= 11.2

which is smaller than the proposed value in the question. Therefore, this cannot be a right triangle.