Question

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

Explanation:

Step1: Use similarity of triangles

Since \(\angle JKL=\angle HKI = 90^{\circ}\) and \(\angle JLK=\angle HIK\) (given equal angles), \(\triangle JKL\sim\triangle HKI\) by AA (Angle - Angle) similarity criterion.
For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{JK}{HK}=\frac{JL}{HI}\).
Here, \(JK = w\), \(HK = 12\), \(JL = 5\), \(HI=15\).

Step2: Substitute values into the ratio

Substitute the values into \(\frac{JK}{HK}=\frac{JL}{HI}\), we get \(\frac{w}{12}=\frac{5}{15}\).
Cross - multiply: \(15w=5\times12\).
Since \(5\times12 = 60\), the equation becomes \(15w = 60\).
Divide both sides by 15: \(w=\frac{60}{15}\).

Answer:

\(4\)