Question

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

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle JIK\sim\triangle JML\) (by AA similarity, as \(\angle J\) is common and \(\angle I=\angle M = 90^{\circ}\)), the ratios of corresponding sides are equal. That is \(\frac{JI}{JM}=\frac{IK}{ML}\).
Here, \(JI = 15\) m, \(JM=15 + 15=30\) m, \(ML = 16\) m and \(IK = u\).

Step2: Substitute values into the proportion

Substitute the values into \(\frac{JI}{JM}=\frac{IK}{ML}\), we get \(\frac{15}{30}=\frac{u}{16}\).
Cross - multiply: \(30u=15\times16\).
Then \(30u = 240\).
Solve for \(u\): \(u=\frac{240}{30}\).

Answer:

\(u = 8\) meters