Question

The perimeter of two similar triangles are 10 cm and 15 cm respectively, find the ratio of their areas.

• A. 3:4
• B. 4:9
• C. 3:2
• D. 2:1

Hint:

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides or perimeters.

Answer 1

The Correct Option is B

Step 1: Use the property of similar triangles.
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. If the ratio of their perimeters is \( \frac{10}{15} \), then the ratio of their areas will be the square of this ratio.
Step 2: Find the ratio of the sides.
The ratio of the perimeters of the two triangles is: \[ \frac{10}{15} = \frac{2}{3} \]
Step 3: Find the ratio of the areas.
The ratio of the areas will be the square of the ratio of the sides: \[ \left( \frac{2}{3} \right)^2 = \frac{4}{9} \]
Step 4: Conclusion.
Thus, the ratio of the areas of the two triangles is \( 4:9 \). Therefore, the correct answer is (B).