A) 1: 2: 3
B) 2: 3: 4
C) 3: 4: 5
D) 4: 5: 6
Correct Answer: C
Solution :
Let the sides of the triangle be\[a-d,\ a,\ a+d\], then hypotenuse being the greatest side\[i.e.\]\[a+d\]. So, \[{{(a+d)}^{2}}={{a}^{2}}+{{(a-d)}^{2}}\] \[\Rightarrow \]\[{{a}^{2}}+{{d}^{2}}+2ad={{a}^{2}}+{{a}^{2}}-2ad+{{d}^{2}}\Rightarrow a=4d\] Therefore ratio of the side \[s=a-d:a:a+d\] \[=(4d-d)\ :\ 4d:(4d+d)=3:4:5\].
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