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
David B.
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.

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