How do you use the Pythagorean Theorem to determine if the following three numbers could represent the measures of the sides of a right triangle: 20, 6, 21?

2 Answers
Apr 18, 2017

The Pythagorean Theorem tells us that a triangle has a right angle if and only if the length of the longest side (the "hypotenuse") squared is equal to the some of the squares of the other two sides.


In this case, if the triangle were a right-angled triangle
#21^2# would need to be equal to #6^2+20^2#

Without doing the actual calculation we can see that
#color(white)("XXX")21^2# is an odd number, and
#color(white)("XXX")6^2+20^2# is an even number
so these values can not be equal (and the triangle does not contain a right angle)>

Apr 18, 2017

Pythagorean Theorem refers to right-angled triangles.


In a right angled triangle, the square of the hypotenuse is equal to
the sum of the squares of the other two sides.

#a^2 + b^2 = c^2#

C will be the longest side of the triangle, in this case, 21

#20^2 + 6^2 = 436#

However, #21^2 = 441#

Hence, it is not a right-angled triangle.