Final answer:
To find missing dimensions, scale factors represent proportional relationships, where dimensions of drawings or models can be converted to actual sizes by multiplication or division. Comparing areas involves square factors, a squared scale factor times the area of the smaller shape to find the missing dimension.
Step-by-step explanation:
Scale Factors and Dimensions
To answer the schoolwork question regarding the finding missing dimensions using factoring and scale factors, let's look at a couple of examples.
Understanding Scale Factors
When scaling objects in drawings or models, a scale factor is used to determine the proportional increase or decrease in size. It's necessary to have a consistent way to convert measurements from one scale to another.
Scale Factor from Drawing to Actual Size: To find the actual size when you have the drawing size and the scale factor, you multiply the drawing dimensions by the scale factor.
Scale Factor from Actual Size to Drawing: Conversely, to find the scale drawing size from the actual size, you would divide the actual dimensions by the scale factor.
Proportional Relationships
For instance, if a scale factor is given as "2 inches:3 feet" and the scale measurement is 6 inches, you would use the proportion 2/6 = x/36 (3 feet equals 36 inches), where x is the missing actual dimension in inches. You would solve for x to find the actual dimensions of the object.
Comparing Areas with Scale Factors
When comparing the areas of two similar shapes, like squares or rectangles, with a scale factor between them, one can determine the missing dimension by setting up a proportion based on the known dimensions and scale factor. If the scale factor of the side lengths is known, the area of the larger shape will be the square of the scale factor times the area of the smaller shape.
For example, if one square has sides twice as long as another, the area of the larger square will be four times (2 squared) the area of the smaller square.