Question

in the diagram below, \\( \triangle hij sim \triangle hkl \\). find s.

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

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle HIJ\) and \(\triangle HKL\), the ratios of corresponding sides are equal. That is \(\frac{HI}{HK}=\frac{HJ}{HL}\). Let \(HJ = s\) and \(HL=36\) yd, \(HI = 6\) yd, \(HK = 24\) yd.

Step2: Substitute values into the proportion

Substitute the values into \(\frac{HI}{HK}=\frac{HJ}{HL}\), we get \(\frac{6}{24}=\frac{s}{36}\).

Step3: Solve for \(s\)

Cross - multiply: \(24s=6\times36\). Then \(24s = 216\). Divide both sides by 24: \(s=\frac{216}{24}=9\).

Answer:

\(9\)