What is the ratio of the areas of two similar triangles if their scale factor is 2:1?

Step 1: The problem states that two similar triangles have a scale factor of 2:1. Step 2: For similar figures, the ratio of their areas is the square of their scale factor. Let the scale factor be k. Then k = 2/1. Step 3: Calculate the ratio of the areas. Ratio of areas = (Scale factor)²; Ratio of areas = (2/1)²; Ratio of areas = (2²)/(1²); Ratio of areas = 4/1 The ratio of the areas of the two similar triangles is 4:1. 4:1

What is the ratio of the areas of two similar triangles if their scale factor is 2:1?

Step 1: The problem states that two similar triangles have a scale factor of 2:1. Step 2: For similar figures, the ratio of their areas is the square of their scale factor. Let the scale factor be k. Then k = 2/1. Step 3: Calculate the ratio of the areas. Ratio of areas = (Scale factor)²; Ratio of areas = (2/1)²; Ratio of areas = (2²)/(1²); Ratio of areas = 4/1 The ratio of the areas of the two similar triangles is 4:1. 4:1

Solved: What is the ratio of the areas of two similar…

The problem states that two similar triangles have a scale factor of $2:1$.
For similar figures, the ratio of their areas is the square of their scale factor.
Let the scale factor be $k$ . Then $k = \frac{2}{1}$ .
Calculate the ratio of the areas.
Ratio of areas $= (\text{Scale factor})^2$
Ratio of areas $= \left(\frac{2}{1}\right)^2$
Ratio of areas $= \frac{2^2}{1^2}$
Ratio of areas $= \frac{4}{1}$

The ratio of the areas of the two similar triangles is $4:1$ .

4:1

What is the ratio of the areas of two similar triangles if their scale factor is 2:1?

Answer

Step-by-step solution

The problem states that two similar triangles have a scale factor of $2:1$.

For similar figures, the ratio of their areas is the square of their scale factor.

Calculate the ratio of the areas.

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