Question

In the given Figure, $△ABC\sim △$ $PQR$ and quad $ABCD$ $\sim$ quad $PQRS$. Determine the values of $x,y,z$ in each case.

Answer 1

$△ABC\sim △PQR$

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$

$\therefore$ $\frac{12}{9}=\frac{7}{x}=\frac{10}{y}$

$\Rightarrow$ $\frac{12}{9}=\frac{7}{x}$

$\therefore$ $x=5.25$

$\Rightarrow$ $\frac{12}{9}=\frac{10}{y}$

$\therefore$ $y=7.5$

Now, $QuadABCD\sim QuadPQRS$

Then, $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CD}{RS}=\frac{AD}{PS}$

$\frac{16}{x}=\frac{50}{y}=\frac{\frac{50}{3}}{z}=\frac{20}{7}$

$\Rightarrow$ $\frac{16}{x}=\frac{20}{7}$

$\therefore$ $x=5.6$

$\Rightarrow$ $\frac{50}{y}=\frac{20}{7}$

$\therefore$ $y=17.5$

$\Rightarrow$ $\frac{50}{3z}=\frac{20}{7}$

$\Rightarrow$ $3z=17.5$

$\Rightarrow$ $z=5.83$