Question : The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.
Option 1: 6 : 13
Option 2: 2 : 3
Option 3: 9 : 4
Option 4: 35 : 24
Correct Answer: 9 : 4
Solution :
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In this case, the corresponding sides are in the ratio of the perimeters. So, the ratio of the areas of the two triangles is:
$\left(\frac{36}{24}\right)^2 = \left(\frac{3}{2}\right)^2 = \frac{9}{4}=9:4$
Hence, the correct answer is 9 : 4.
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