If two triangles are similar, what is the ratio of their corresponding sides if

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Question: If two triangles are similar, what is the ratio of their corresponding sides if the ratio of their areas is 9:16?

Options:

Correct Answer: 3:4

Solution:

The ratio of the sides of similar triangles is the square root of the ratio of their areas. sqrt(9:16) = 3:4.

If two triangles are similar, what is the ratio of their corresponding sides if the ratio of their areas is 9:16?

If two triangles are similar, what is the ratio of their corresponding sides if the ratio of their areas is 9:16?

Step 1: Understand that similar triangles have corresponding sides that are in proportion.
Step 2: Know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 3: Given the ratio of the areas is 9:16, write it as a fraction: 9/16.
Step 4: To find the ratio of the sides, take the square root of the area ratio: sqrt(9/16).
Step 5: Calculate the square root of 9, which is 3, and the square root of 16, which is 4.
Step 6: Write the ratio of the sides as 3:4.

Similarity of Triangles – When two triangles are similar, their corresponding sides are in proportion, and the ratio of their areas is the square of the ratio of their corresponding sides.
Area Ratio and Side Ratio Relationship – The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.