Question

Triangles $ABC$ and $PQR$ are similar. What is the length of $QR$?

• A. $12$
• B. $10$
• C. $15$
• D. $7$

Answer 1

The correct option is C $15$

Because the triangles are similar, corresponding angles are congruent and corresponding sides are proportional.
First find the scale factor:
Since $AC=12$ and $PR=18$, the scale factor is found by dividing $PR$ by $AC$
Scale factor $=$ $\frac{18}{12}$ $=1.5$
(That means that the second triangle is $1.5$ times as large as the first)
Now use the same scale factor to find the length of $QR$:
$QR=1.5\times 10=15$