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Question
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 60, 61
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Solution
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.
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