Question : Which of the following sets of lengths (in cm) will give three sides of an obtuse-angled triangle?
Option 1: 15, 62, 64
Option 2: 17, 64, 66
Option 3: 16, 63, 65
Option 4: 18, 65, 67
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Correct Answer: 15, 62, 64
Solution : For an obtuse-angled triangle, P 2 + B 2 < H 2 Checking the options: 1) 15 2 + 62 2 = 4069 < 64 2 2) 17 2 + 64 2 = 4385 > 66 2 3) 16 2 + 63 2 = 4225 = 65 2 4) 18 2 + 65 2 = 4549 > 67 2 Only option (1) satisfies. Hence, the correct answer is 15, 62, 64.
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