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प्रश्न
The sides of the triangle are given below. Find out which one is the right-angled triangle?
8, 15, 17
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उत्तर
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 8, 15, and 17.
Let us check whether the given set (8, 15, 17) forms a Pythagorean triplet or not.
The biggest number among the given set is 17.
(17)2 = 289; (15)2 = 225; (8)2 = 64
Now, 225 + 64 = 289
∴ (15)2 + (8)2 = (17)2
Thus, (8, 15, 17) forms a Pythagorean triplet.
Hence, the given triangle with sides 8, 15, and 17 is a right-angled triangle.
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