Question

In the given figure, $AB||CD||EF$ given $AB=7.5cm$ $DC=ycm$ $EF=4.5cm$, $BC=xcm$. Find the value of $x$ and $y$

Answer 1

Consider $△ACB$ and $△CEF$

Both triangles are similar

$\therefore \frac{AB}{EF}=\frac{x}{3}$

$\Rightarrow \frac{7.5}{4.5}=\frac{x}{3}$

$x=\frac{7.5}{4.5}\times 3$

$\therefore x=5$cm

Consider $△BCD$ and $△BFE$

$\frac{x}{y}=\frac{x+3}{4.5}$

$\frac{5}{y}=\frac{5+3}{4.5}$

$\Rightarrow y=\frac{5\times 4.5}{8}$

$\therefore y=\frac{45}{16}$cm