Question

If \( \triangle ABC \) and \( \triangle PQR \) are similar triangles in which \( AD \) is perpendicular from vertex \( A \) to \( BC \) and \( PT \) is perpendicular from vertex \( P \) to \( QR \), \( AD = 9 \, \text{cm} \) and \( PT = 7 \, \text{cm} \), then the ratio of areas of triangle \( \triangle AB \) and triangle \( \triangle PQR \) is

• A. 9:7
• B. 7:9
• C. 16:25
• D. 81:49

Hint:

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding heights.

Answer 1

The Correct Option is D

Step 1: Since the triangles are similar, the ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Step 2: The ratio of the corresponding heights is \( \frac{AD}{PT} = \frac{9}{7} \). Step 3: The ratio of the areas is the square of the ratio of the corresponding heights: \[ \left( \frac{9}{7} \right)^2 = \frac{81}{49} \] Thus, the correct answer is \( 81:49 \).