Question

$△ABC$ is similar to $△XYZ$. Length of $AB,BC,CA$ are 3 cm, 4 cm and 5 cm respectively. Find the length of $YZ$ and $XZ$ if $XY=9cm$.

• A. 6 cm and 8 cm
• B. 9 cm and 12 cm
• C. 9 cm and 15 cm
• D. 12 cm and 15 cm

Answer 1

The correct option is D 12 cm and 15 cm

As two triangles are similar, their sides will be in proportion.
We know,
$△ABC\sim △XYZ$ and $XY=9cm$
$\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}$

$\frac{3}{9}=\frac{BC}{YZ}=\frac{AC}{XZ}$

$\frac{1}{3}=\frac{4}{YZ}=\frac{5}{XZ}$

$⟹\frac{1}{3}=\frac{4}{YZ}$ and $\frac{1}{3}$ = $\frac{5}{XZ}$

$YZ=3\times 4$ and $XZ=3\times 5$
$YZ=12cm$ and $XZ=15cm$