Question

find the missing length. the triangles in each pair are similar.

1. $\triangle abc \sim \triangle akl$

10)
11)

1. $\triangle rst \sim \triangle abc$

Explanation:

Step1: Use the property of similar triangles (corresponding sides are proportional)

For \(\triangle ABC\sim\triangle AKL\), we have \(\frac{AB}{AL}=\frac{AC}{AK}\). Let \(AL = x\). Then \(\frac{65}{x}=\frac{60}{52}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(60x=65\times52\). So \(x=\frac{65\times52}{60}=\frac{65\times13}{15}=\frac{845}{15}=\frac{169}{3}\approx56.33\).

Answer:

\(\frac{169}{3}\)