A) 4
B) 6
C) 5
D) 8
Correct Answer: D
Solution :
\[N{{G}^{2}}+G{{D}^{2}}=N{{D}^{2}}\] [by Pythagoras theorem] \[\Rightarrow \,\,\,{{x}^{2}}+{{\left( x+7 \right)}^{2}}={{17}^{2}}\] \[\Rightarrow \,\,{{x}^{2}}+{{x}^{2}}+49+14x=289\] \[\Rightarrow \,\,2{{x}^{2}}+14x-240=0\] \[\Rightarrow {{x}^{2}}+7x-120=0\] \[\Rightarrow {{x}^{2}}+15x-8x-120=0\] \[\Rightarrow \left( x-8 \right)\left( x+15 \right)=0\] \[\Rightarrow \,\,x\left( x+15 \right)-8\left( x-15 \right)=0\] \[x=8\] \[x=-15\] (Not possible)
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