Question #16a92

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Question #16a92

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Answer 1 · 2017-08-18T12:57:14

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 · 2017-08-18T15:01:09

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.

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Question #16a92

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