Question

25 which of the following triangles is similar to \\( \triangle p q r \\)?

Explanation:

Step1: Calculate the ratio of sides for \(\triangle PQR\)

For \(\triangle PQR\), assume the sides are \(a = 18\) and \(b = 21\).

Step2: Check the ratio for each option

• Option A: Sides \(12\) and \(15\). The ratio \(\frac{12}{15}=\frac{4}{5}\), for \(\triangle PQR\) \(\frac{18}{21}=\frac{6}{7}\). Not equal.
• Option B: Sides \(6\) and \(10\). The ratio \(\frac{6}{10}=\frac{3}{5}\), for \(\triangle PQR\) \(\frac{18}{21}=\frac{6}{7}\). Not equal.
• Option C: Sides \(15\) and \(17.5\). The ratio \(\frac{15}{17.5}=\frac{15\times2}{17.5\times2}=\frac{30}{35}=\frac{6}{7}\), for \(\triangle PQR\) \(\frac{18}{21}=\frac{6}{7}\). Equal.
• Option D: Sides \(9\) and \(12\). The ratio \(\frac{9}{12}=\frac{3}{4}\), for \(\triangle PQR\) \(\frac{18}{21}=\frac{6}{7}\). Not equal.

Answer:

C.