Question

find r.

write your answer as a whole number or a decimal. do not round.

r = \boxed{} meters

Explanation:

Step1: Identify similar triangles

Triangles \( KLJ \) and \( KMN \) are similar (by AA similarity, as both are right - angled and share \( \angle K \)).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{r}{12}=\frac{12}{12 + 4}\) (the ratio of the height of the smaller triangle to the height of the larger triangle is equal to the ratio of the base of the smaller triangle to the base of the larger triangle).
Simplify the denominator: \(12+4 = 16\). So the proportion is \(\frac{r}{12}=\frac{12}{16}\).

Step3: Solve for \( r \)

Cross - multiply: \(16r=12\times12\).
Calculate \(12\times12 = 144\). Then \(r=\frac{144}{16}\).
Simplify \(\frac{144}{16}=9\).

Answer:

9