Question

The sides of the triangle are given below. Find out which one is the right-angled triangle?

11, 60, 61

Answer 1

It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet. If the lengths of the sides of a triangle form such a triplet, then the triangle is a right-angled triangle.

The sides of the given triangle are 11, 60, and 61.

Let us check whether the given set (11, 60, 61) forms a Pythagorean triplet or not.
The biggest number among the given set is 61.

(61)² = 3721; (11)² = 121; (60)² = 3600

Now, 121 + 3600 = 3721

∴ (11)² + (60)² = (61)²

Thus, (11, 60, 61) forms a Pythagorean triplet.

Hence, the given triangle with sides 11, 60, and 61 is a right-angled triangle.