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
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
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The ratio of the areas of two similar triangles is the square of the ratio of their corresponding heights.
Updated On: Oct 27, 2025
- 9:7
- 7:9
- 16:25
- 81:49
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The Correct Option is D
Solution and Explanation
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 \( 81:49 \).
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