Question

Which of the following can be the sides of a right angled triangle ?

• A. $35,17,18$
• B. $39,19,18$
• C. $35,27,18$
• D. $41,40,9$

Answer 1

The correct option is D $41,40,9$

We know that in a right angle triangle,

The sum of the squares on two sides of a triangle is equal to the square on the third side, then the triangle is a right angle.

$Bas{e}^2+Prependicula{r}^2=Hypotenus{e}^2$

Now, we go to the options,

A) ${18}^2+{17}^2$ is not equal to ${35}^2$ so leave this option.

B) ${19}^2+{18}^2$ is not equal to ${39}^2$ so leave this option.

C) ${27}^2+{18}^2$ is not equal to ${35}^2$ so leave this option.

D)${40}^2+9^2$ is equal to ${41}^2$ so right this option.

Hence, all option is incorrect.

Now , we take the triplet $41$,$40$ ,$9$

${40}^2+9^2=1681$

$40^2+9^2=41^2$

Hence, $41$,$40$,$9$ are the sides of a right angle triangle

option $D$ is correct.