If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

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Question: If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

Options:

Correct Answer: 9:16

Solution:

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

If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

Step 1: Understand that the triangles are similar because they have sides in a specific ratio.
Step 2: Identify the ratio of the sides of the triangles, which is 3:4.
Step 3: Remember that the ratio of the areas of similar triangles is found by squaring the ratio of their sides.
Step 4: Square the ratio of the sides: (3:4)² means you square both numbers in the ratio.
Step 5: Calculate 3² = 9 and 4² = 16.
Step 6: Write the new ratio of the areas as 9:16.

Ratio of Areas – The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
Similar Triangles – Triangles are similar if their corresponding angles are equal and their sides are in proportion.