Question

if these two shapes are similar, what is the measure of the missing length q?
1 ft
q
3 ft
9 ft
q = \boxed{} feet

Explanation:

Step1: Identify the scale factor

Since the shapes are similar, the ratio of corresponding sides is equal. The side of length 1 ft in the small triangle corresponds to 3 ft in the large triangle. So the scale factor from small to large is $\frac{3}{1} = 3$.

Step2: Find the missing length \( q \)

The side of length \( q \) in the small triangle corresponds to 9 ft in the large triangle. Using the scale factor, we can set up the proportion $\frac{q}{9} = \frac{1}{3}$. Cross - multiplying gives \( 3q=9\times1 \), so \( q = \frac{9}{3}=3 \).

Answer:

3