Scale and similar shapes
Solve problems involving similar shapes where the scale factor is known or can be found
What a learner can do afterwards
- Find the missing side of a similar rectangle given a scale factor of 3
- Determine the scale factor between two similar triangles from given side lengths
- Use a scale factor to enlarge or reduce a shape and verify that all sides are in the same ratio
1 · Read
Two shapes are similar when they have the exact same shape but different sizes. Every side on the small shape matches a side on the big shape, and all the matching sides are stretched by the same amount. That amount is called the scale factor.
A small rectangle is 4 cm by 6 cm. It is enlarged with a scale factor of 3. Multiply each side by 3: 4 x 3 = 12 cm and 6 x 3 = 18 cm. The new rectangle is 12 cm by 18 cm, and both sides grew by the same scale factor.
To find a missing side, multiply the small shape's side by the scale factor. To find the scale factor itself, divide a big shape's side by the matching small shape's side.
This works for any similar shapes, including triangles, squares, and other polygons. Just make sure you compare matching sides, the ones in the same position on each shape.
Similar shapes have matching sides in the same ratio, so multiply by the scale factor to enlarge and divide to find it.
More to read
How to Find the Scale Factor (With Example Problems)
A scale factor tells you how much bigger or smaller one shape is compared to another shape that looks exactly the same, just a different size. Shapes like this are called similar shapes.
Here is how to find a scale factor: 1. Check that the two shapes are similar. Their angles match, and every side grows or shrinks by the same amount. 2. Pick a side on the small shape and find the side that matches it on the big shape. 3. Divide the big side by the small side. That number is your scale factor.
Once you know the scale factor, you can find any missing side. Multiply a side on the small shape by the scale factor to get the matching side on the big shape. Or divide a side on the big shape by the scale factor to get the small one.
Try it: a small rectangle has a side of 4 cm, and the matching side on a similar big rectangle is 12 cm. The scale factor is 12 divided by 4, which is 3.
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