In the given figure, we have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, Calculate the values of x and y.

Solution:

It is given that $A B\|C D\| E F$.

$A B=6 \mathrm{~cm}, C D=x \mathrm{~cm}$ and $E F=10 \mathrm{~cm}$

We have to calculate the values of $x$ and $y$.

In $\triangle A D B$ and $\triangle D E F$, we have

$\angle A D B=\angle E D F \quad$ (Vertically opposite angles)

$\Rightarrow \angle A B D=\angle D E F \quad$ (Alternate interior angles)

So $\triangle A D B \sim \triangle D E F$

EFAB=DEDB

$\frac{10 \mathrm{~cm}}{6 \mathrm{~cm}}=\frac{y}{4 \mathrm{~cm}}$

$6 \mathrm{~cm} \times y=40 \mathrm{~cm}$

$y=\frac{40 \mathrm{~cm}}{6 \mathrm{~cm}}$

$y=6.67 \mathrm{~cm}$

Similarly in $\triangle A B E$ we have

$\mathrm{DCAB}=\mathrm{DEBE} \Rightarrow \mathrm{x} 6=\mathrm{y} 4+\mathrm{y} \Rightarrow \mathrm{x}=6 \mathrm{y} 4+\mathrm{y} \Rightarrow \mathrm{x}=6 \times 6.674+6.67 \Rightarrow \mathrm{x}=3.75$

Hence, $\mathrm{x}=3.75 \mathrm{~cm}$ and $y=6.67 \mathrm{~cm}$