Difference between revisions of "Find Scale Factor"
m (importing article from wikihow) |
m (Text replacement - "[[Category:M" to "[[Category: M") |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
The scale factor, or linear scale factor, is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are different sizes. The scale factor is used to solve basic geometric problems. You can use the scale factor to find the missing side lengths of a figure. Conversely, you can use the side lengths of two similar figures to calculate the scale factor. These problems involve multiplication or require you to simplify fractions. | The scale factor, or linear scale factor, is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are different sizes. The scale factor is used to solve basic geometric problems. You can use the scale factor to find the missing side lengths of a figure. Conversely, you can use the side lengths of two similar figures to calculate the scale factor. These problems involve multiplication or require you to simplify fractions. | ||
| − | [[Category:Mathematics]] | + | [[Category: Mathematics]] |
==Steps== | ==Steps== | ||
===Finding the Scale Factor of Similar Figures=== | ===Finding the Scale Factor of Similar Figures=== | ||
| − | #Verify that the figures are similar. Similar figures, or shapes, are ones in which the angles are congruent, and the side lengths are in proportion. Similar figures are the same shape, only one figure is bigger than the other.<ref>http://www.mathsisfun.com/geometry/similar.html</ref> | + | #Verify that the figures are similar. Similar figures, or shapes, are ones in which the angles are congruent, and the side lengths are in proportion. Similar figures are the same shape, only one figure is bigger than the other.<ref name="rf1">http://www.mathsisfun.com/geometry/similar.html</ref> |
#*The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other. | #*The problem should tell you that the shapes are similar, or it might show you that the angles are the same, and otherwise indicate that the side lengths are proportional, to scale, or that they correspond to each other. | ||
| − | #Find a corresponding side length on each figure. You may need to rotate or flip the figure so that the two shapes align and you can identify the corresponding side lengths. You should be given the length of these two sides, or should be able to measure them.<ref>http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures</ref> If you do not know at least one side length of each figure, you cannot find the scale factor. | + | #Find a corresponding side length on each figure. You may need to rotate or flip the figure so that the two shapes align and you can identify the corresponding side lengths. You should be given the length of these two sides, or should be able to measure them.<ref name="rf2">http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures</ref> If you do not know at least one side length of each figure, you cannot find the scale factor. |
#*For example, you might have a triangle with a base that is 15 cm long, and a similar triangle with a base that is 10 cm long. | #*For example, you might have a triangle with a base that is 15 cm long, and a similar triangle with a base that is 10 cm long. | ||
| − | #Set up a ratio. For each pair of similar figures, there are two scale factors: one you use when scaling up, and one you use when scaling down. If you are scaling up from a smaller figure to a larger one, use the ratio <math>\text{Scale Factor} = \frac{larger length}{smaller length}</math>. If you are scaling down from a larger figure to a smaller one, use the ratio <math>\text{Scale Factor} = \frac{smaller length}{larger length}</math>.<ref>http://www.bbc.co.uk/education/guides/zpwycdm/revision/2</ref> | + | #Set up a ratio. For each pair of similar figures, there are two scale factors: one you use when scaling up, and one you use when scaling down. If you are scaling up from a smaller figure to a larger one, use the ratio <math>\text{Scale Factor} = \frac{larger length}{smaller length}</math>. If you are scaling down from a larger figure to a smaller one, use the ratio <math>\text{Scale Factor} = \frac{smaller length}{larger length}</math>.<ref name="rf3">http://www.bbc.co.uk/education/guides/zpwycdm/revision/2</ref> |
#*For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio <math>\text{Scale Factor} = \frac{smaller length}{larger length}</math>.<br>Filling in the appropriate values, it becomes <math>\text{Scale Factor} = \frac{10}{15}</math>. | #*For example if you are scaling down from a triangle with a 15 cm base to one with a 10 cm base, you would use the ratio <math>\text{Scale Factor} = \frac{smaller length}{larger length}</math>.<br>Filling in the appropriate values, it becomes <math>\text{Scale Factor} = \frac{10}{15}</math>. | ||
| − | #Simplify the ratio. The [[Simplify a Ratio | simplified ratio,]] or fraction, will give you your scale factor. If you are scaling down, your scale factor will be a proper fraction.<ref | + | #Simplify the ratio. The [[Simplify a Ratio | simplified ratio,]] or fraction, will give you your scale factor. If you are scaling down, your scale factor will be a proper fraction.<ref name="rf2" /> If you are scaling up, it will be a whole number or improper fraction, which you can convert to a decimal. |
#*For example, the ratio <math>\frac{10}{15}</math> simplifies to <math>\frac{2}{3}</math>. So the scale factor of two triangles, one with a base of 15 cm and one with a base of 10 cm, is <math>\frac{2}{3}</math>. | #*For example, the ratio <math>\frac{10}{15}</math> simplifies to <math>\frac{2}{3}</math>. So the scale factor of two triangles, one with a base of 15 cm and one with a base of 10 cm, is <math>\frac{2}{3}</math>. | ||
| Line 18: | Line 18: | ||
#Determine whether you are scaling up or down. If you are scaling up, your missing figure will be larger, and the scale factor will be a whole number, improper fraction, or decimal. If you are scaling down your missing figure will be smaller, and your scale factor will most likely be a proper fraction. | #Determine whether you are scaling up or down. If you are scaling up, your missing figure will be larger, and the scale factor will be a whole number, improper fraction, or decimal. If you are scaling down your missing figure will be smaller, and your scale factor will most likely be a proper fraction. | ||
#*For example, if the scale factor is 2, then you are scaling up, and the similar figure will be larger than the one you have. | #*For example, if the scale factor is 2, then you are scaling up, and the similar figure will be larger than the one you have. | ||
| − | #Multiply one side length by the scale factor. The scale factor should be given to you. When you multiply the side length by the scale factor, this gives you the missing corresponding side length on the similar figure.<ref>http://www.virtualnerd.com/pre-algebra/ratios-proportions/missing-measurements-similar-figures-scale-factor.php</ref> | + | #Multiply one side length by the scale factor. The scale factor should be given to you. When you multiply the side length by the scale factor, this gives you the missing corresponding side length on the similar figure.<ref name="rf4">http://www.virtualnerd.com/pre-algebra/ratios-proportions/missing-measurements-similar-figures-scale-factor.php</ref> |
#*For example, if the hypotenuse of a right triangle is 5 cm long, and the scale factor is 2, to find the hypotenuse of the similar triangle, you would calculate <math>5 | #*For example, if the hypotenuse of a right triangle is 5 cm long, and the scale factor is 2, to find the hypotenuse of the similar triangle, you would calculate <math>5 | ||
\times 2 = 10</math>. So the similar triangle has a hypotenuse that is 10 cm long. | \times 2 = 10</math>. So the similar triangle has a hypotenuse that is 10 cm long. | ||
| Line 29: | Line 29: | ||
#*Simplify the ratio. The ratio <math>\frac{54}{6}</math> simplifies to <math>\frac{9}{1} = 9</math>. The ratio <math>\frac{6}{54}</math> simplifies to <math>\frac{1}{9}</math>. So the two rectangles have a scale factor of <math>9</math> or <math>\frac{1}{9}</math>. | #*Simplify the ratio. The ratio <math>\frac{54}{6}</math> simplifies to <math>\frac{9}{1} = 9</math>. The ratio <math>\frac{6}{54}</math> simplifies to <math>\frac{1}{9}</math>. So the two rectangles have a scale factor of <math>9</math> or <math>\frac{1}{9}</math>. | ||
#Try this problem. An irregular polygon is 14 cm long at its widest point. A similar irregular polygon is 8 inches at its widest point. What is the scale factor? | #Try this problem. An irregular polygon is 14 cm long at its widest point. A similar irregular polygon is 8 inches at its widest point. What is the scale factor? | ||
| − | #*Irregular figures can be similar if all of their sides are in proportion. Thus, you can calculate a scale factor using any dimension you are given.<ref>http://www.vias.org/physics/bk1_03_02b.html</ref> | + | #*Irregular figures can be similar if all of their sides are in proportion. Thus, you can calculate a scale factor using any dimension you are given.<ref name="rf5">http://www.vias.org/physics/bk1_03_02b.html</ref> |
#*Since you know the width of each polygon, you can set up a ratio comparing them. Scaling up, the ratio is <math>\text{Scale Factor} = \frac{14}{8}</math>. Scaling down, the ratio is <math>\text{Scale Factor} = \frac{8}{14}</math>. | #*Since you know the width of each polygon, you can set up a ratio comparing them. Scaling up, the ratio is <math>\text{Scale Factor} = \frac{14}{8}</math>. Scaling down, the ratio is <math>\text{Scale Factor} = \frac{8}{14}</math>. | ||
#*Simplify the ratio. The ratio <math>\frac{14}{8}</math> simplifies to <math>\frac{7}{4} = 1\frac{3}{4} = 1.75</math>. The ratio <math>\frac{8}{14}</math> simplifies to <math>\frac{4}{7}</math>. So the two irregular polygons have a scale factor of <math>1.75</math> or <math>\frac{4}{7}</math>. | #*Simplify the ratio. The ratio <math>\frac{14}{8}</math> simplifies to <math>\frac{7}{4} = 1\frac{3}{4} = 1.75</math>. The ratio <math>\frac{8}{14}</math> simplifies to <math>\frac{4}{7}</math>. So the two irregular polygons have a scale factor of <math>1.75</math> or <math>\frac{4}{7}</math>. | ||
