# Question 16a92

Aug 18, 2017

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.

Aug 18, 2017

The sides are in the ratio $\text{ "9" ":" "40" ":" } 41$

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:

$3 \text{ ":" "4" ":" } 5$

$5 \text{ ":" "12" ":" } 13$

$7 \text{ ":" "24" ":" } 25$

$8 \text{ ":" "15" ":" } 17$

$9 \text{ ":" "40" ":" } 41$

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

$9 \text{ ":" "40" ":" } 41$

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