Question

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

1.5, 1.6, 1.7

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 1.5, 1.6, and 1.7.

Let us check whether the given set (1.5, 1.6, 1.7) forms a Pythagorean triplet or not.
The biggest number among the given set is 1.7.

(1.7)² = 2.89; (1.5)² = 2.25; (1.6)² = 2.56

Now, 2.25 + 2.56 = 4.81 ≠ 2.89

∴ (1.5)² + (1.6)² ≠ (1.7)²

Thus, (1.5, 1.6, 1.7) does not form a Pythagorean triplet.

Hence, the given triangle with sides 1.5, 1.6, and 1.7 is not a right-angled triangle.