A) 1: 2: 3
B) 2 : 3 : 4
C) 3: 4: 5
D) 4 : 5 : 6
Correct Answer: C
Solution :
Let sides be \[a-d,a,a+d\]and as it is a right angled triangle \[{{(a-d)}^{2}}+{{a}^{2}}={{\left( a+d \right)}^{2}}\] Þ \[{{a}^{2}}+{{d}^{2}}-2ad+{{a}^{2}}={{a}^{2}}+{{d}^{2}}+2ad\] Þ \[a=4d\Rightarrow d=\frac{a}{4}\]. Hence the sides are \[\frac{3a}{4},a,\frac{5a}{4}\] i.e., in ratio 3 : 4 : 5.
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