A) a : b
B) \[(a+3b):(3a+b)\]
C) \[(3a+b):(a+3b)\]
D) \[(2a+b):(3a+b)\]
Correct Answer: C
Solution :
We have, ABCD is a trapezium and let h be the height of ABCD Then, \[\frac{h}{2}\]is the height of trapezium EFBA and EDCF. Now, Area of trapezium EFBA \[=\frac{1}{2}(a+b+EX+YF)\times \frac{h}{2}\] \[=\frac{1}{2}\left( a+b+\frac{a-b}{2} \right)\times \frac{h}{2}\] Similarly, Area of trapezium EFCD \[=\frac{1}{2}(b+b+EX+YF)\times \frac{h}{2}\] \[=\frac{1}{2}\left( 2b\frac{a-b}{2} \right)\times \frac{h}{2}\] \[\therefore \]Required ration \[=\frac{\frac{1}{2}\left( \frac{3a+b}{2} \right)\times \frac{h}{2}}{\frac{1}{2}\left( \frac{3b+a}{2} \right)\times \frac{h}{2}}=\frac{3a+b}{a+3b}\]You need to login to perform this action.
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