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 \[\Delta ABD,\text{ }AO\] is median \[\therefore \,\,\,2\{{{(AO)}^{2}}+{{(DO)}^{2}}\}=A{{B}^{2}}+A{{D}^{2}}\] \[\therefore \,\,\,2({{x}^{2}}+{{5}^{2}})=144+64=208\] \[\therefore \,{{x}^{2}}=79\Rightarrow \,x=8.89\] \[\therefore \,\,AC\,=2\times 8.89=17.78\,cm\]