Question

triangle ijk is similar to triangle lmn. find the measure of side lm. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

In similar triangles \( \triangle IJK \) and \( \triangle LMN \), the sides \( IJ \) and \( LM \) are corresponding, and \( KJ \) and \( NM \) are corresponding. So, the ratios of corresponding sides are equal: \( \frac{IJ}{LM} = \frac{KJ}{NM} \).

Step2: Substitute known values

We know \( IJ = 5 \), \( KJ = 9 \), and \( NM = 40 \). Substitute these into the proportion: \( \frac{5}{LM} = \frac{9}{40} \).

Step3: Solve for \( LM \)

Cross - multiply: \( 9\times LM = 5\times40 \), so \( 9LM = 200 \). Then, \( LM=\frac{200}{9}\approx22.2 \).

Answer:

\( 22.2 \)