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# ACMGM024

## 1.4 Scaling Factor and its Applications

### Similar Figures and Shapes

Two shapes are similar if they share the same shape but not the size.

• Their corresponding angles are equal;
• Their corresponding sides are in the same ratio.

### Calculating the Scaling Factor

• The scaling factor is a numerical value representing the scale of one shape/object to a similar shape (with a different scale).
• The scaling factor can be calculated as the proportional difference between the lengths of the two shapes/objects, the square root of the proportional difference between their areas, or the cubic root of the proportional difference between their volumes:

k=\frac{L_{A}}{L_{B}}=\sqrt{\frac{A_{A}}{A_{B}}}=\sqrt[3]{\frac{V_{A}}{V_{B}}}

Note: this calculates the scaling factor for shape/object A with respect to shape/object B. For example, a scaling factor of 2 means A has twice the length of B.

• The scaling factor is dimensionless (i.e. has no units).
• k>0The scaling factor is larger than 0.
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