Question

in the diagram below, ( \triangle ijksim\triangle lmk ). find ( s ).
write your answer as a whole number or a decimal. do not round.
( s=) meters

Explanation:

Step1: Recall Similar Triangles Property

Since \(\triangle IJK \sim \triangle LMK\), the corresponding sides are proportional. So, \(\frac{IJ}{LM}=\frac{IK}{LK}\).
We know \(IJ = 3\) m, \(LM = 6\) m, \(LK = 10\) m, and \(IK = s\). Also, note that \(LK = 10\) and \(IK = s\), so the ratio of corresponding sides gives \(\frac{3}{6}=\frac{s}{10}\).

Step2: Solve for \(s\)

Cross - multiply the proportion \(\frac{3}{6}=\frac{s}{10}\). We get \(6\times s=3\times10\), which simplifies to \(6s = 30\). Then, divide both sides by 6: \(s=\frac{30}{6}=5\).

Answer:

\(s = 5\) meters