Question

the two triangles shown are similar,
6 cm, 12 cm, 8 cm (small triangle); ? , 18 cm, 12 cm (large triangle). *not drawn to scale.
what is the length of the missing side of the larger triangle?
a. 8 cm
b. 9 cm
c. 10 cm
d. 12 cm

Explanation:

Step1: Find the scale factor

The corresponding sides of similar triangles are proportional. Let's take the base sides: the smaller triangle has a base of 8 cm, and the larger one has a base of 12 cm. The scale factor \( k \) is \( \frac{12}{8}=\frac{3}{2} \).

Step2: Apply the scale factor to the height

The height of the smaller triangle is 6 cm. To find the height of the larger triangle, multiply the smaller height by the scale factor: \( 6\times\frac{3}{2} = 9 \) cm.

Answer:

B. 9 cm