Question

The sides of a triangle are of length 8 cm , 15 cm and 17 cm. Is this triangle a right triangle? If so, which side is the hypotenuse?

Answer 1

We know that the hypotenuse is the longest side. If 8 cm, 15 cm and 17 cm are the lengths of the triangle, then 17 cm will be the hypotenuse.

Using the converse of Pythagoras theorem, we get

${\left(17\right)}^2={\left(15\right)}^2+{\left(8\right)}^2$

⇒ 289 = 225 + 64

⇒ 289 = 289

Since the converse of the pythagoras theorem is proved, the given triangle is right-angled. Among the given three sides 17 cm is the longest side which is the hypotenuse of the triangle.