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Can two squares have the same ratio for their scale factor and the ratio of their areas?
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)
What else can I help you with?
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
What gives the ratio that compares measurements of the drawing to the measurements of the real object?
It is the scale ratio or scale factor
What is the name of the common ratio of corresponding sides of similar figures?
The scale factor.The scale factor.The scale factor.The scale factor.
What is the difference between scale and scale factor?
The scale gives the ratio that compares the measurements of the drawing or model to the measurements of the real object. Scale factor is a scale written as a ratio without units in simplest from.
What is a scale written as a ratio without units in simplest form called?
scale factor
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 the definition of a scale factor?
The ratio of any two corresponding similar geometric figures lengths in two . Note: The ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube of the scale factor. .... (: hope it helped (: .....
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 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.
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.
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.
The diameter of the moon is approximately one fourth of the diameter of the earth find the ratio of their surface areas?
The ratio of the surface areas of two similar objects is equal to the square of the ratio of their corresponding linear dimensions. Since the diameter of the moon is one fourth of the diameter of the Earth, the ratio of their diameters is 1:4. Therefore, the ratio of their surface areas is (1/4)^2 = 1/16. This means that the surface area of the moon is 1/16th of the surface area of the Earth.
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
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 are the areas of similar rectangles related to the scale factor?
The areas are proportional to the square of the scale factor.
Perimeter ratio 100 and find scale factor?
The linear scale factor is 100.
