A) 8 cm
B) 15 cm
C) 23 cm
D) 25 cm
Correct Answer: C
Solution :
Let the sides of the right angled triangle other than hypotenuse be x, x + 7 respectively. Then, \[\Rightarrow \]\[{{x}^{2}}+{{\left( x+7 \right)}^{2}}={{17}^{2}}\] \[\Rightarrow \]\[2{{x}^{2}}+14x+49-289=0\] \[\Rightarrow \]\[\,{{x}^{2}}+7x-120=0\] \[\Rightarrow \]\[{{x}^{2}}+15x-8x-120=0\] \[\Rightarrow \]\[\left( x+15 \right)\left( x-8 \right)=0\Rightarrow x=8,-15\] Sum of the two sides \[=2x+7=2\times 8+7=\mathbf{23}\]
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