The areas of the squares created by the side lengths of the triangle are shown. Which best explains whether this triangle is a right triangle? 9sqrt 12sqrt 15sqrt

Question

asked Jan 3, 2021 90.6k views

2 Answers

David Lechner · Answer 1 · 2021-01-09T16:19:38+0000

Answer:

Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because
$9+12\\eq 15$

Explanation:

The complete question in the attached figure

we know that

If the length sides of a triangle, satisfy the Pythagorean Theorem, then is a right triangle

c^2=a^2+b^2

where

c is the hypotenuse (the greater side)

a and b are the legs

In this problem

The length sides squared of the triangle are equal to the areas of the squares

so

$c^2=15\ in^2$

$a^2=12\ in^2$

$b^2=9\ in^2$

substitute

15=12+9

15=21 ----> is not true

so

The length sides not satisfy the Pythagorean Theorem

therefore

Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because
$9+12\\eq 15$