Question

If a triangle has sides 6, 8, and 10, is it acute, right, or obtuse?

Answer 1

A `6:8:10` triangle is a right triangle.

Explanation:

Either recognize that `6:8:10` is a simple multiple of the standard `3:4:5` right triangle

or

Take the sum of the squares of the shorter two sides:
`color(white)("XXX")6^2+8^2=36+64=100`
and
the square of the longest side
`color(white)("XXX")10^2=100`

Since these are equal, by the Pythagorean Theorem, the triangle is a right triangle. (if the square of the longest side had been greater the triangle would have been obtuse; if it had been smaller, the triangle would have been acute).