Question

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?

Answer 1

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.

Explanation:

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)>

Answer 2

Pythagorean Theorem refers to right-angled triangles.

Explanation:

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.

https://www.youtube.com/watch?time_continue=1&v=bWpY6iVYgI4