Question

triangle jkl is similar to triangle mno. find the measure of side no. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since \(\triangle JKL \sim \triangle MNO\), the sides are proportional. Let \(JK = 16\), \(MN = 49\), \(KL = 25\), and we need to find \(NO\). The corresponding sides are \(JK\) and \(MN\), \(KL\) and \(NO\).

Step2: Set up proportion

The proportion for similar triangles is \(\frac{JK}{MN}=\frac{KL}{NO}\). Substituting the known values: \(\frac{16}{49}=\frac{25}{NO}\).

Step3: Solve for \(NO\)

Cross - multiply: \(16\times NO = 49\times25\). Then \(NO=\frac{49\times25}{16}\). Calculate \(49\times25 = 1225\), so \(NO=\frac{1225}{16}=76.5625\approx76.6\) (rounded to the nearest tenth).

Answer:

\(76.6\)