question_answer

            The area of an isosceles trapezium is \[176\text{ }c{{m}^{2}}\] and the height is 2/11th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is [SSC CGL Tier II, 2015]

A) 24

B) \[2\sqrt{137}\]

C) \[\sqrt{137}\]

D) 28

Correct Answer: B

Solution :

[b]                         Given, Area of trapezium \[=(4x)(2x)+(2x)(1.5x)=1.76{{M}^{2}}\]\[\Rightarrow \]\[\times =4\] Diagonal            \[=\sqrt{{{(2\times 4)}^{2}}+{{(5.5\times 4)}^{2}}}\] \[=\sqrt{64+484}=\sqrt{548}=2\sqrt{137}\]