Question

triangle jkl is similar to triangle mno. find om. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

(images of triangles jkl and mno with side lengths: jkl has jl=23, jk=14; mno has mn=57, om=x)

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle JKL \sim \triangle MNO\), corresponding sides are proportional. So, \(\frac{JL}{OM}=\frac{JK}{MN}\). Here, \(JL = 23\), \(JK = 14\), \(MN = 57\), and \(OM = x\).

Step2: Set Up Proportion

Substitute values into the proportion: \(\frac{23}{x}=\frac{14}{57}\).

Step3: Cross - Multiply and Solve

Cross - multiply: \(14x = 23\times57\). Calculate \(23\times57 = 1311\). Then, \(x=\frac{1311}{14}\approx93.6\).

Answer:

\(93.6\)