Question : Which of the following ratios can be the ratio of the sides of a right-angled triangle?
Option 1: 9 : 6 : 3
Option 2: 13 : 12 : 5
Option 3: 7 : 6 : 5
Option 4: 5 : 3 : 2
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Correct Answer: 13 : 12 : 5
Solution : By Pythagoras theorem, In a right-angled triangle, the sum of squares of the length of smaller sides = square of the length of the largest side. By trial and error, 9 2 $\neq$6 2 + 3 2 7 2 $\neq$6 2 + 5 2 5 2 $\neq$3 2 + 2 2 12 2 + 5 2 = 144 + 25 = 169 = 13 2 So, 13 : 12 : 5 is the ratio of the sides of a right-angled triangle. Hence, the correct answer is 13 : 12 : 5.
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