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Question

ABCDis a trapezium in which ABIICD. If ADC is equal to twice ABC, AD=acm and CD=bcm, then find the length of AB.


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Solution

Finding the length of AB:

Given:

ABCD is a trapezium withAB||CD.

ABC+ADC=180°

From the given details we know that

ADC=2(ABC)

ABC+2(ABC)=180º

3(ABC)=180º

ABC=180º3=60º

Let us draw perpendiculars from the vertices D,Cto AB, namely DE andCF

From the figure, DEis perpendicular toAB, then triangle ADE is formed withDAE=60°.

cos60º=12=AEAD

Hence,

AE=AD2=a2

EFis equal toCD=b

AB=AE+EF+FB

=a2+b+a2=(a2+a2)+b=a+b

Therefore the length of AB is a+b


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