Question

1. triangle klm is similar to triangle rtu. the triangles are shown with side lengths in centimeters. what is the length of side ru in centimeters?

move the correct answer to the box. not all answers will be used.
the length of side ru is

Explanation:

Step1: Set up the proportion

Since \(\triangle KLM\sim\triangle RTU\), the ratios of corresponding sides are equal. Let \(RU = x\). Then \(\frac{KL}{RT}=\frac{LM}{TU}\). Substituting the values: \(\frac{10}{2\frac{1}{2}}=\frac{12}{3}\) (This is wrong, correct proportion is \(\frac{LM}{TU}=\frac{KM}{RU}\)). The correct proportion is \(\frac{LM}{TU}=\frac{KM}{RU}\), where \(LM = 12\), \(TU=3\), \(KM = 14\), and \(RU=x\). So \(\frac{12}{3}=\frac{14}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(12x=3\times14\).

Step3: Solve for \(x\)

\(12x = 42\), then \(x=\frac{42}{12}=\frac{7}{2}=3\frac{1}{2}\)

Answer:

\(3\frac{1}{2}\)