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Question

In the given pentagon, ratio of area of trapezium ABCD to area of BEC is 5:2 and AG = 6 cm, EF = 4 cm. Find the length of BC if AD = 6 cm.


A
6 cm
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B
8 cm
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C
9 cm
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D
10 cm
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Solution

The correct option is C 9 cm
Area of trapezium ABCD
= 12×(Sum of parallel sides)×height
= 12×(AD+BC)×AG
= 12×(6+BC)×6
= 3×(6+BC)

Area of BEC = 12×base×height
= 12×BC×EF
= 12×BC×4
= BC×2

According to given condition,
area of ABCDarea of BEC=523×(6+BC)BC×2=526+BCBC=533×(6+BC)=5×BC18+3(BC)=5(BC)18=2(BC)BC=182=9 cm

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