Q: How is the scale factor the same as the ratio of the area?

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The sacle factor between two shapes is the same as the ratio of their perimeters.

The area changes by the square of the same factor.

Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .

It is the same as 2 cm = 3 m or 1 cm = 1.5 m The scale ratio would therefore be 150:1

To divide the numerator and the denominator of a ratio by the same factor means to simplify or reduce the ratio. This is done by dividing both numbers in the ratio by their greatest common factor, which results in an equivalent ratio.

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It is the scale factor.

The sacle factor between two shapes is the same as the ratio of their perimeters.

The area changes by the square of the same factor.

Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .

Let a represent the scale factor of the two squares. Then it follows that the ratio of the areas is a^2. If these are equal, you get the equation a = a^2, and this is only true for a=0 or a=1. However, the only applicable value for a here is 1. In short, yes, they can, but only if both the scale factor and the ratio of the areas are equal to 1 (i.e. the squares are congruent)

It is the same as 2 cm = 3 m or 1 cm = 1.5 m The scale ratio would therefore be 150:1

To divide the numerator and the denominator of a ratio by the same factor means to simplify or reduce the ratio. This is done by dividing both numbers in the ratio by their greatest common factor, which results in an equivalent ratio.

If you change the scale factor of a geometric figure by a factor "x", that is, keeping the new figure similar to the old one, the perimeter (which is also a linear measurement) will change by the SAME factor "x".Note that any area will change by a factor of x squared.

The perimeter will scale by the same factor.

To find the new area, you have to multiply the original area by the square of the scale change. For example, you have a rectangle with adjacent sides of 3 and 4. Another rectangle has the same dimensions but with triple the scale. The original rectangle's area is 12. Multiply that by 9, which is the square of the new scale, and you get an area of 108. That matches up with the area of the new rectangle, which has adjacent sides of 12 and 9.

It is simplifying the ratio.

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