question_answer

A parallelogram, the length of whose sides are 12 cm and 8 cm has one diagonal 10 cm long. The length of the other diagonal is:

A) 8.89 cm

B) 17.78 cm

C) 18.18 cm

D) 9.00 cm

E) None of these  

Correct Answer: B

Solution :

Explanation Option (b) is correct. Let AC = 2x cm Then AO = x In \[\Delta ABD,\,\,AO\]is median \[\therefore \,\,2\{{{(AO)}^{2}}+{{(DO)}^{2}}\}=A{{B}^{2}}+A{{D}^{2}}\] \[\therefore \,\,2({{x}^{2}}+{{5}^{2}})=144+64=208\] \[\therefore \,\,\,\,\,\,\,\,{{x}^{2}}=79\Rightarrow x=8.89\] \[\therefore \,AC=2\times 8.89=17.78\,\,cm\]