Question

For $△ABC$ and $△XYZ$, $△ABC\leftrightarrow △XYZ$ is a similarity. If $\frac{AB}{4}=\frac{BC}{6}=\frac{CA}{3}$, $AC=3$, $XY=5$, find $YZ$ and $XZ$.

Answer 1

$Giventhat△ABC\sim △XYZ$

$\frac{AB}{4}=\frac{BC}{6}=\frac{AC}{3}=k$

$\therefore AB=4k;BC=6k;AC=3k$

$XY=5$

$⟹\frac{AB}{XY}=\frac{BC}{YZ}$

$⟹\frac{4k}{5}=\frac{6k}{YZ}$

$\therefore YZ=\frac{(6k\times 5)}{4k}$

$\therefore YZ=\frac{15}{2}=7.5$

$\frac{AB}{XY}=\frac{AC}{XZ}implies\frac{4k}{5}=\frac{3k}{XZ}$

$\therefore YZ=7.5\&XZ=3.75$