If two triangles are similar, what is the ratio of their areas if the ratio of t

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Question: If two triangles are similar, what is the ratio of their areas 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.

If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:4?

If two triangles are similar, what is the ratio of their areas if the ratio of their corresponding sides is 3:4?

Step 1: Understand that similar triangles have the same shape but different sizes.
Step 2: Know that the ratio of their corresponding sides is given as 3:4.
Step 3: To find the ratio of their areas, we need to square the ratio of their sides.
Step 4: Calculate (3/4) squared, which means (3/4) * (3/4).
Step 5: Multiply the numerators: 3 * 3 = 9.
Step 6: Multiply the denominators: 4 * 4 = 16.
Step 7: So, the ratio of the areas of the two triangles is 9:16.

Similarity of Triangles – Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
Area Ratio of Similar Figures – The ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions (sides).