In the figure, given alongside, AB, CD and EF are
parallel lines. Given AB = 7.5 cm, DC = y cm, EF
= 4.5 cm, BC = x cm and CE = 3 cm, calculate the
values of x and y
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Answer:
In △BCD and △BEF,
∠DBC=∠FBE (Common angle)
∠BCD=∠BEF (Corresponding angles of parallel lines CD and EF)
∠BDC=∠BFE (Corresponding angles of parallel lines CD and EF)
Thus, △BCD∼△BEF (AAA rule)
Hence,
BE
BC
=
BF
BD
=
EF
CD
(Corresponding sides)
x+3
x
=
BF
BD
=
4.5
y
..(I)
Similarly, △FCD∼△FAB
Thus,
FA
FC
=
AB
CD
=
FB
FD
7.5
y
=
BF
DF
(II)
From I and II,
BD=
4.5
y
BF and DF=
7.5
y
BF
BD+DF=BF
4.5
y
BF+
7.5
y
BF=BF
7.5y+4.5y=7.5×4.5
y=
16
45
Also,
x+3
x
=
4.5
y
x+3
x
=
16×4.5
45
x+3
x
=
72
45
72x=45x+135
27x=135
x=5cm
Step-by-step explanation:
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