Question

The sides of a triangle are 4cm, 60cm, 61cm. Verify that it is a right angle triangle or not.

Answer 1

Hint: All rights triangles follow Pythagoras theorem, that is, ${H^2} = {P^2} + {B^2}$, where $H$ is the hypotenuse of the right triangle, $P$ is the perpendicular and $B$ is the base of the triangle. Also, hypotenuse is the longest side of the right triangle. Substitute $H = 61$ , 60 as perpendicular and 4 as base in ${H^2} = {P^2} + {B^2}$. If the equality holds, then the given sides represent a right triangle.

Complete step-by-step answer:
As we know, Pythagoras theorem holds for all right triangles. Pythagoras theorem states that in a right triangle, ${H^2} = {P^2} + {B^2}$, where $H$ is the hypotenuse of the right triangle, $P$ is the perpendicular and $B$ is the base of the triangle.
While deciding the length of hypotenuse, we know that hypotenuse is the longest side of the right triangle. So, let $H = 61$ from the given sides.
Perpendicular and base can take any value from the left values of sides.
Let, $P = 60$ and $B = 4$.
Substitute these values in Pythagoras theorem, ${H^2} = {P^2} + {B^2}$ to check whether the given sides satisfy the equation or not.
$
  {\left( {61} \right)^2}\mathop = \limits^? {\left( {60} \right)^2} + {\left( 4 \right)^2} \\
  3721\mathop = \limits^? 3600 + 16 \\
$
$3721 = 3616{\text{ }}$🗶
After substituting the values, we get an equation that is incorrect.
Hence, the given sides are not the sides of the right triangle.

Note: Pythagoras theorem is only valid for right triangles. Also, hypotenuse is the longest side in a right triangle. Perpendicular and base of the right triangle intersect each other at right angles. The numbers which satisfy Pythagoras theorem are together known as Pythagorean triple.