Question

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

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle IHK\sim\triangle JLK\) (by AA similarity, as \(\angle H=\angle JLK = 90^{\circ}\) and \(\angle K\) is common). For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{IH}{JL}=\frac{HK}{LK}\).
Given \(IH = 0.9\) m, \(HK=1.2\) m, \(LK = 0.4\) m, and \(JL=c\).
Substituting the values into the proportion \(\frac{0.9}{c}=\frac{1.2}{0.4}\).

Step2: Solve the proportion for \(c\)

Cross - multiply: \(1.2c=0.9\times0.4\).
First, calculate \(0.9\times0.4 = 0.36\). Then the equation becomes \(1.2c=0.36\).
Divide both sides by \(1.2\): \(c=\frac{0.36}{1.2}\).
\(c = 0.3\).

Answer:

\(0.3\)