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Question

In the figure given below AB, CD, and EF are parallel lines. Given AB = 9 cm, DC = y cm, EF = 4.5 cm, BC = x cm, and CE = 3 cm. The value of 'x' and 'y' are:


A

6 cm and 3 cm respectively

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B

6 cm and 5 cm respectively

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C

3 cm and 6 cm respectively

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D

4.5 cm and 3 cm respectively

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Solution

The correct option is A

6 cm and 3 cm respectively


In ΔBFE&BDC
B=B (common angle)
BDC=BFE (corresponding angle)
ΔBFE ΔBDC (AA similarity criterion)

So, BCBE=CDEF=BDBF (Ratio of corresponding sides are equal in similar triangles)
xx+3=y4.5=BDBF ------ (1)

In ΔFDC & ΔFBA
F=F (common)
FDC=FBA (corresponding angle)
FDC ΔFBA (AA similarity criterion)

So, FDBF=y7.5 ------- (2)

From (1) we have BDBF=y4.5 ------- (3)

Adding (2) and (3), we get
FDBF+BDBF=y7.5+y4.5FD+BDBF=y(17.5+14.5)BFBF=y(4.5+7.57.5×4.5)y=7.5×4.512=33.7512=4516 cm

From (1) we have,

xx+3=y4.5 xx+3=4516×4.5 xx+3=58 8x=5x+15 x=5 cm


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