If two triangles have sides in the ratio 3:4, what can be said about their areas

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Question: If two triangles have sides in the ratio 3:4, what can be said about their areas?

Options:

Correct Answer: The areas are in the ratio 9:16.

Solution:

The areas of similar triangles are in the ratio of the squares of their corresponding sides. Therefore, (3:4)² = 9:16.

If two triangles have sides in the ratio 3:4, what can be said about their areas?

If two triangles have sides in the ratio 3:4, what can be said about their areas?

Step 1: Understand that the triangles have sides in the ratio 3:4.
Step 2: Recognize that this means for every 3 units of one triangle's side, the other triangle's corresponding side is 4 units.
Step 3: Know that when triangles are similar, their areas relate to the square of the ratio of their sides.
Step 4: Calculate the square of the side ratio: (3:4)² means you square both numbers: 3² = 9 and 4² = 16.
Step 5: Write the area ratio as 9:16, which means the area of the first triangle is to the area of the second triangle as 9 is to 16.

Ratio of Sides – Understanding that the ratio of the sides of two triangles can be used to determine the ratio of their areas.
Area of Similar Triangles – Knowing that the areas of similar triangles are proportional to the squares of the ratios of their corresponding sides.