Question

If a triangle is dilated by scale factor n, what is the relationship between the areas of those two triangles?

Answer 1

When a triangle is dilated by a scale factor of n, the area of the larger triangle will be n² times the area of the smaller triangle.

Step-by-step explanation:

When a triangle is dilated by a scale factor of n, the relationship between the areas of the two triangles is given by the square of the scale factor. This means that the area of the larger triangle will be n² times the area of the smaller triangle. For example, if the scale factor is 2, the area of the larger triangle will be 2² = 4 times the area of the smaller triangle.

Answer 2

When a triangle is dilated by a scale factor of n, the area of the resulting triangle will be n² times larger than the original triangle's area. This general rule applies to all similar figures, where the ratio of their areas is the square of the scale factor.

Step-by-step explanation:

If a triangle is dilated by scale factor n, the relationship between the areas of the original triangle and the dilated triangle is consequential to the scale factor squared. To explain, the dimension of the area is represented as L² (length squared). So, when the linear dimensions of a figure are multiplied by the scale factor n, every length is multiplied by n, resulting in the area being multiplied by n². For instance, if the scale factor is 2, the new area will be 2², or 4 times the original area.

Considering two squares where one is a dilation of the other with a scale factor of 2, we can see that the area of the larger square will be 4 times larger than that of the smaller square. This illustrates the general rule of the ratio of the areas of similar figures being the square of the scale factor.