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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