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Question
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
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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 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.
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