Question

In the given figure, we have AB $\parallel$ CD $\parallel$ EF. If AB = 6 cm, CD = x BD = 4 cm and DE = y cm, calculate the value of x and y.

Answer 1

Consider $△ADB$ and $△EDF$,

$\angle ADB=\angle EDF$ [ Vertical angles ]

$\angle ABD=\angle FED$ [ Alternate angles ]

$\angle BAD=\angle EFD$ [ Alternate angles ]

$\therefore$ $△ADB\sim △EDF$ [ By ASA criterion ]

$\Rightarrow$ $\frac{BD}{DE}=\frac{AB}{FE}$

$\Rightarrow$ $\frac{4}{y}=\frac{6}{10}$

$\Rightarrow$ $6y=40$

$\Rightarrow$ $y=\frac{40}{6}=\frac{20}{3}$

$\Rightarrow$ $y=6.67cm$

Similarly, $△ADE\sim △CDE$ [ AA criterion ]

$\Rightarrow$ $\frac{DE}{BE}=\frac{DC}{BA}$

$\Rightarrow$ $\frac{6.67}{10.67}=\frac{x}{6}$

$\Rightarrow$$x=6\times \frac{6.67}{10.67}$

$\Rightarrow$ $x=3.75cm$

$\therefore$ The values of $x$ and $y$ are $3.75cm$ and

$6.67cm$.