Question

In the figure, given below $AB,CD$ and $EF$ parallel lines. Given $AB=7.5cm,DC=ycm,EF=4\cdot 5cm,BC=xcm$ and $CE=3cm$ calculate the values of $x$ and $y$.

Answer 1

In $\Delta BEF\Rightarrow BD/DE=BC/CE$

$BD/DE=X/3$

$BD=xDF=3$

$\Delta FBA\Rightarrow FD/CD=FB/AD$

$\frac{FD}{CD}=\frac{FD+DB}{AB}$

$3/y=x+\frac{3}{7.5}$

$\Delta BEF\Rightarrow BC/CD=BC/EF\Rightarrow \frac{x}{y}=x+\frac{3}{4\cdot 5}$

by using the eq.

$x^2-2x-15=0$

$x=5$ and $x=-3$

$y=\frac{4\cdot 5\times 5}{5+3}=2\cdot 8125$