Question

figure jklmn and figure pqrst, shown below, are similar figures. the scale factor of figure jklmn to figure pqrst is 3:2. if kl = 18 cm and mn = 30 cm, what is the length of side qr? a. 20 cm b. 45 cm c. 27 cm d. 12 cm

Explanation:

Step1: Recall scale - factor formula

For similar figures, the ratio of corresponding side lengths is equal to the scale factor. Let the length of side $QR$ be $x$. The scale factor of figure $JKLMN$ to figure $PQRS$ is $\frac{3}{2}$, and $KL$ corresponds to $QR$. So, $\frac{KL}{QR}=\frac{3}{2}$.

Step2: Substitute known values

We know that $KL = 18$ cm. Substituting into the equation $\frac{KL}{QR}=\frac{3}{2}$, we get $\frac{18}{x}=\frac{3}{2}$.

Step3: Cross - multiply and solve for $x$

Cross - multiplying gives $3x=18\times2$. Then $3x = 36$, and dividing both sides by 3, we have $x = 12$ cm.

Answer:

D. 12 cm