Question

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

Explanation:

Step1: Determine the similarity of triangles

Since \( \angle H = \angle L = 90^{\circ}\) and \( \angle x\) is common to both \(\triangle xHJ\) and \(\triangle xLK\), by the AA (Angle - Angle) similarity criterion, \(\triangle xHJ\sim\triangle xLK\).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. We know that \(\frac{xJ}{xK}=\frac{HJ}{LK}\). Given \(xJ = 15\space m\), \(xK=xJ + JK=15 + 5=20\space m\), and \(LK = 12\space m\). Let \(HJ = w\). Then the proportion is \(\frac{15}{20}=\frac{w}{12}\).

Step3: Solve for \(w\)

Cross - multiply: \(20w=15\times12\). So \(20w = 180\). Then \(w=\frac{180}{20}=9\).

Answer:

\(9\)