Question

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

40, 20, 30

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 40, 20, and 30.

Let us check whether the given set (40, 20, 30) forms a Pythagorean triplet or not.
The biggest number among the given set is 40.

(40)² = 1600; (20)² = 400; (30)² = 900

Now, 400 + 900 = 1300 ≠ 1600

∴ (20)² + (30)² ≠ (40)²

Thus, (40, 20, 30) does not form a Pythagorean triplet.

Hence, the given triangle with sides 40, 20, and 30 is not a right-angled triangle.