What is the ratio of the areas of two similar triangles if the ratio of their co

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Question: What is the ratio of the areas of two similar triangles if the ratio of their corresponding sides is 3:4?

Options:

Correct Answer: 9:16

Solution:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)^2 = 9/16.

What is the ratio of the areas of two similar triangles if the ratio of their corresponding sides is 3:4?

What is the ratio of the areas of two similar triangles if the ratio of their corresponding sides is 3:4?

Step 1: Understand that the triangles are similar, which means their shapes are the same but their sizes are different.
Step 2: Note the ratio of the corresponding sides of the triangles, which is given as 3:4.
Step 3: Recognize that to find the ratio of the areas of similar triangles, you need to square the ratio of their corresponding sides.
Step 4: Calculate the square of the ratio 3:4. This means you take (3/4) and multiply it by itself: (3/4) * (3/4).
Step 5: Perform the multiplication: 3 * 3 = 9 (for the numerator) and 4 * 4 = 16 (for the denominator).
Step 6: Write the result as a fraction: 9/16. This is the ratio of the areas of the two similar triangles.

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