If two triangles are similar and the ratio of their corresponding sides is 3:5,

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Question: If two triangles are similar and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?

Options:

Correct Answer: 9:25

Solution:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (3/5)² = 9/25.

If two triangles are similar and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?

If two triangles are similar and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?

Step 1: Understand that similar triangles have the same shape but different sizes.
Step 2: Note the given ratio of the corresponding sides of the triangles, which is 3:5.
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 3:5. This means you calculate (3/5)².
Step 5: Perform the calculation: (3/5)² = 3² / 5² = 9 / 25.
Step 6: Conclude that the ratio of the areas of the two triangles is 9:25.

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).