Question

△cba ~ △clk
find the length of \\(\overline{al}\\):
answer

Explanation:

Step1: Identify similar triangles ratio

Since \(\triangle CBA \sim \triangle CLK\), the ratios of corresponding sides are equal. Let \(AC = x\), then \(AL = AC + CL=x + 14\). The ratio of \(CB\) to \(CK\) is \(\frac{36}{8}=\frac{9}{2}\), and the ratio of \(AC\) to \(CL\) should be the same, so \(\frac{x}{14}=\frac{9}{2}\).

Step2: Solve for \(AC\)

Cross - multiply: \(2x=14\times9 = 126\), then \(x=\frac{126}{2}=63\).

Step3: Calculate \(AL\)

\(AL=AC + CL=63 + 14 = 77\).

Answer:

\(77\)