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
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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