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

The scale factor between two similar figures is the ratio of their corresponding linear dimensions (lengths). When calculating the area of similar figures, the area ratio is equal to the square of the scale factor, since area is a two-dimensional measurement. Thus, if the scale factor is ( k ), the ratio of the areas is ( k^2 ). This relationship illustrates that while the scale factor pertains to linear dimensions, the area ratio reflects the effect of that scaling in two dimensions.


Does the same relationship between the scale factor of similar rectangles and their area apply for similar triangles?

Yes, the same relationship between the scale factor and area applies to similar triangles. If two triangles are similar, the ratio of their corresponding side lengths (the scale factor) is the same, and the ratio of their areas is the square of the scale factor. For example, if the scale factor is ( k ), then the area ratio will be ( k^2 ). This principle holds true for all similar geometric shapes, including rectangles and triangles.


What does scale factor of two similar figures tell you about area?

If the sides of two shapes have a scale factor of sf:1, then their areas will be in the ratio of sf2: 1.


Perimeter ratio 100 and find scale factor?

The linear scale factor is 100.


What is the area of a trangle with scale factor of two thirds?

With similar objects (where one is an exact scale version of the other) then if the linear measurements are in the ratio 2 : 3 then the areas are in the ratio 22 : 32 which equals 4 : 9. So if the sides of two triangles have a scale factor of 2/3 then the areas have a scale factor of 4/9.

Related Questions

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

The scale factor between two similar figures is the ratio of their corresponding linear dimensions (lengths). When calculating the area of similar figures, the area ratio is equal to the square of the scale factor, since area is a two-dimensional measurement. Thus, if the scale factor is ( k ), the ratio of the areas is ( k^2 ). This relationship illustrates that while the scale factor pertains to linear dimensions, the area ratio reflects the effect of that scaling in two dimensions.


Does the same relationship between the scale factor of similar rectangles and their area apply for similar triangles?

Yes, the same relationship between the scale factor and area applies to similar triangles. If two triangles are similar, the ratio of their corresponding side lengths (the scale factor) is the same, and the ratio of their areas is the square of the scale factor. For example, if the scale factor is ( k ), then the area ratio will be ( k^2 ). This principle holds true for all similar geometric shapes, including rectangles and triangles.


How is scale factor related to a ratio?

A scale factor is the ratio of corresponding linear measures of two objects.A scale factor is the ratio of corresponding linear measures of two objects.A scale factor is the ratio of corresponding linear measures of two objects.A scale factor is the ratio of corresponding linear measures of two objects.


When applied to a triangle a dilation with a positive scale factor does not preserve to what?

The perimeter to area ratio.


What does scale factor of two similar figures tell you about area?

If the sides of two shapes have a scale factor of sf:1, then their areas will be in the ratio of sf2: 1.


Two similar triangles have a scale factor of 35 What is the ratio of their areas?

Their scale factor is 3 : 5, which mean their sides scale factor is 3 : 5, too. The area formula : S = bh/2 ---> The ratio of their areas : (3 : 5)^2=9 : 25 It's the answer.


What is a scale written as a ratio called?

scale factor


What is the difference between scale factor and scale ratio?

if two polygons are similar, then the ratio of the length of 2 corresponding sides is called a scale factor


Perimeter ratio 100 and find scale factor?

The linear scale factor is 100.


What is a scale written as a ratio in simplest form?

scale factor


What is the area of a trangle with scale factor of two thirds?

With similar objects (where one is an exact scale version of the other) then if the linear measurements are in the ratio 2 : 3 then the areas are in the ratio 22 : 32 which equals 4 : 9. So if the sides of two triangles have a scale factor of 2/3 then the areas have a scale factor of 4/9.


How do you find scale factor?

# is the ratio of the demensions in the drawing to the corresponding actual dimensions. The scale factor for a scale drawing is the ratio of the dimensions in the drawing to the corresponding acual bimensions.