Question

$△ABC$ is similar to $△XYZ$ by $SAS$ similarity. If in $△ABC$ $AB=12,BC=8,\angle B={60}^o$
and in $△XYZ$ $XY=3$,$\angle Y={60}^o$. Find the value of $YZ$

• A. $15$
• B. $20$
• C. $4$
• D. $2$

Answer 1

The correct option is D $2$

If two triangles are similar, then their corresponding sides are proportional.

Given $△ABC\sim △XYZ$

$⟹\frac{AB}{XY}=\frac{BC}{YZ}$

$⟹\frac{12}{3}=\frac{8}{YZ}$

$⟹YZ=\frac{3\times 8}{12}$

$⟹YZ=2$