Question

in the diagram below, \\( \triangle lhi \sim \triangle jhk \\). find \\( s \\).

write your answer as a whole number or a decimal. do not round.
\\( s = \square \\) feet

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle LHI\sim\triangle JHK\), the ratios of corresponding sides are equal. That is \(\frac{LI}{JK}=\frac{HI}{HK}\).
Given \(LI = 5\) ft, \(HI=4\) ft, \(HK = 8\) ft, and \(JK=s\).

Step2: Substitute values into the proportion

Substitute the values into \(\frac{LI}{JK}=\frac{HI}{HK}\), we get \(\frac{5}{s}=\frac{4}{8}\).
Cross - multiply: \(4s=5\times8\).

Step3: Solve for \(s\)

\(4s = 40\), then \(s=\frac{40}{4}\).

Answer:

\(s = 10\) feet