Question

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

11, 12, 15

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, 12, and 15.

Let us check whether the given set (11, 12, 15) forms a Pythagorean triplet or not.
The biggest number among the given set is 15.

(15)² = 225; (11)² = 121; (12)² = 144

Now, 121 + 144 = 265 ≠ 225

∴ (11)² + (12)² ≠ (15)²

Thus, (11, 12, 15) does not form a Pythagorean triplet.

Hence, the given triangle with sides 8, 15, and 17 is not a right-angled triangle.