The sides of certain triangles are given below. Determine which of them are right triangles.
(ii) $a\ =\ 9\ cm,\ b\ =\ 16\ cm$ and $c\ =\ 18\ cm$

Given:

The sides of a triangle are $a=9\ cm, b=16\ cm$, and $c=18\ cm$.

To do:

We have to determine whether the triangle is a right-angled triangle.

Solution:

$a=9\ cm$

$b=16\ cm$

$c=18\ cm$

We know that,

If the square of the hypotenuse is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle. 

Therefore,

$(a)^2=(9\ cm)^2=81\ cm^2$

$(b)^2=(16\ cm)^2=256\ cm^2$

$(c)^2=(18\ cm)^2=324\ cm^2$

Here, $(a)^2+(b)^2=(81+256)\ cm^2=337\ cm^2$

$(a)^2+(b)^2≠(c)^2$

Therefore, by the converse of Pythagoras theorem, the given sides cannot be the sides of a right triangle.

Tutorialspoint

e

Updated on: 10-Oct-2022

28 Views

Kickstart Your Career

Get certified by completing the course

Get Started