Question

Question #16a92

Answer 1

Yup.

Explanation:

It's a right triangle if `x^2 + y^2 = z^2`, where z is the longest side.

`18^2 = 324, 80^2 = 6400`, so the length of those two sides (squared) adds up to 6724.

`82^2 = 6724`. So, this is a right triangle.

Answer 2

The sides are in the ratio `" "9" ":" "40" ":" "41`

This is one of the Pythagorean Tiples, which means that the triangle is right-angled.

Explanation:

A knowledge of some of the Pythagorean Triples is useful in answering this question.

A Pythagorean Triple is a ratio representing the lengths of the sides of a right-angled triangle, where the sides are all whole numbers and exact. They only apply if there is `90°` angle in the triangle.

Some of the common triples are:

`3" ":" "4" ":" "5`

`5" ":" "12" ":" "13`

`7" ":" "24" ":" "25`

`8" ":" "15" ":" "17`

`9" ":" "40" ":" "41`

The sides of the given triangle are `18m : 80m : 82m`
If these are written as a ratio in the simplest form we get:

`9" ":" "40" ":" "41`

This is one of the Pythagorean Tiples, which means that the triangle is right-angled.