# Using the Pythagorean Theorem, is a triangle with sides abc a right triangle? a=12, b=9, c=15

Jul 2, 2018

Yes. It’s a right triangle.

#### Explanation:

As per Pythagoras theorem,
$\sqrt{{3}^{2} + {4}^{2}} = \sqrt{25} = 5$

If the sides are in the ratio 3 : 4 : 5, then the triangle is a right triangle.

In the given sum, sides are in the ratio, 9 : 12 : 15 which is equivalent to 3 : 4 : 5.

Hence it’s aright triangle as per Pythagoras theorem.

Jul 2, 2018

${12}^{2} + {9}^{2} = {15}^{2}$

$144 + 81 = 225$

$225 = 225$

Yes it is a Pythagorean triangle