Question

let \\( \triangle dot \sim \triangle pan \\). find the missing side \\( x \\).
\\( x = \square \\) m (type an integer or a fraction.)

Explanation:

Step1: Identify Similar Triangles

Since \(\triangle DOT \sim \triangle PAN\) (given by the notation \(\triangle DOT - \triangle PAN\)), their corresponding sides are proportional.

Step2: Set Up Proportion

Let's assume the sides \(DO = 12\) m, \(PA = 8\) m, \(PN = 26\) m, and \(DT = x\) m. The proportion of corresponding sides is \(\frac{DO}{PA}=\frac{DT}{PN}\).
Substituting the known values: \(\frac{12}{8}=\frac{x}{26}\)

Step3: Solve for \(x\)

Cross - multiply: \(8x = 12\times26\)
Calculate \(12\times26 = 312\), so \(8x=312\)
Divide both sides by 8: \(x=\frac{312}{8}=\frac{39}{1}=39\)

Answer:

\(39\)