Question

use the information given in the figure to find the length ln. if applicable, round your answer to the nearest whole number. the lengths on the figure are not drawn accurately.

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle LKN\sim\triangle MKN\) (by AA similarity, as \(\angle N\) is common and both are right - angled triangles), we can use the proportion \(\frac{LK}{MK}=\frac{LN}{MN}\). Let \(LN = x\), then \(LM=x - 20\).

Step2: Substitute the values into the proportion

We know \(LK = 35\), \(MK = 29\), and \(MN=20\). The proportion becomes \(\frac{35}{29}=\frac{x}{20}\).

Step3: Solve for \(x\)

Cross - multiply: \(29x=35\times20\). So \(29x = 700\), and \(x=\frac{700}{29}\approx24.14\). Rounding to the nearest whole number.

Answer:

\(24\)