Question:
If the ratio of corresponding sides of two similar triangles is 4: 9, then the ratio of areas of these triangles is
If the ratio of corresponding sides of two similar triangles is 4: 9, then the ratio of areas of these triangles is
Updated On: Apr 17, 2025
- 16:81
- 4:9
- 2:3
- \(\sqrt{2}:\sqrt{3}\)
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The Correct Option is A
Solution and Explanation
To solve the problem, we need to find the ratio of areas of two similar triangles when the ratio of their corresponding sides is given.
1. Understanding the Area Ratio for Similar Triangles:
If two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Let the ratio of sides be $ \frac{4}{9} $, then:
$ \frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{4}{9} \right)^2 $
2. Squaring the Side Ratio:
$ \left( \frac{4}{9} \right)^2 = \frac{16}{81} $
Final Answer:
The ratio of the areas of the triangles is $ 16 : 81 $
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