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Question

In the figure, seg AB seg DC. Using the information given in the figure, find the value of x.


Solution

Given: Seg ABSeg DCIn DOC and BOA,DCO=BAO          [Alternate angles]CDO=ABO          [Alternate angles ]Therefore, by AA similarity test, DOC ~BOAHence, DOBO=OCOA=CDABDOBO=OCOA3x-3=x-53x-19Cross-multiplying, we get:  3(3x-19)=(x-5)(x-3)9x-57=x2-3x-5x+159x-57=x2-8x+15x2-17x+72=0x2-9x-8x+72=0x(x-9)-8(x-9)=0(x-8)(x-9)=0x=8  or x=9

Mathematics
Mathematics (Geometry)
Standard X

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