question_answer

ABCD is a trapezium, such that \[AB=CD,\] \[AD||BC,\] \[AD=7\text{ }cm\] and\[BC=11\,cm\]. If area of trapezium ABCD is \[54\text{ }sq\text{ }cm,\] then value of CD is-

A)  \[\sqrt{29}\,cm\]                       

B)  \[2\sqrt{10}\,cm\]

C)  \[\sqrt{21}\,cm\]                       

D)  None of these

Correct Answer: B

Solution :

   \[AB=CD\] and \[AD||BC\] \[AD||BC\] [Given] So, \[BF=EC\] and \[AD=EF\] \[EF=AD=7\text{ }cm\] \[BF=EC=\frac{BC-EF}{2}=\frac{11-7}{2}=2\,cm\] Area of trapezium  \[ABCD=54\,c{{m}^{2}}\] \[\frac{(AD+BC)}{2}\times ED=54=\frac{(7+11)}{2}\times ED=54\] \[ED=\frac{54\times 2}{18}=6\,cm\] In \[\Delta \,\,CDE,\,\,C{{D}^{2}}={{(EC)}^{2}}+{{(DE)}^{2}}\] \[C{{D}^{2}}={{(2)}^{2}}+{{(6)}^{2}}=40,\,CD=\sqrt{40}\] \[=\,\,\underline{\,\mathbf{2}\sqrt{\mathbf{10}}\,\,\mathbf{cm}}\]