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Question

In Figure , AB=BC. If the area of ABE is x, calculate the area of ACD.
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A
x2
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B
x3
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C
2x
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D
3x
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E
4x
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Solution

The correct option is E 4x

AB=BC ....Given

So, AB:AC=1:2 ...(I)

BED+BEA=180o ...Angles in linear pair

118o+BEA=180o

BEA=62o=CDA ...(II)

In ABE and ACD

A is the common angle.

BEA=CDA ... from (II)

ABEACD ....AAA test of similarity

So, A(ABE)A(ACD)=(ABAC)2 ....Theorem on ratio of areas of similar triangles

A(ABE)A(ACD)=(12)2

xA(ACD)=14

A(ACD)=4x sq. units


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