A triangle is dilated using a scale factor of 4. The image is then dilated using a scale factor of 3. What scale factor could you use to dilate the original triangle to get the final image?

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A triangle is dilated using a scale factor of 4. The image is then dilated using a scale factor of 3. What scale factor could you use to dilate the original triangle to get the final image?

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Answer 1 · 2015-11-27T03:36:16

For perimeter, the scale factor would be $\frac{a}{b}$ $a/b$ for enlargement, where $a$ $a$ is the perimeter of the dilated triangle and $b$ $b$ is the perimeter of the smaller triangle.
For area, the scale factor would be $\sqrt{\frac{x}{y}}$ $sqrt(x/y)$ for enlargement, where $x$ $x$ is the area of the dilated triangle and $y$ $y$ is the area of the smaller triangle.

Explanation:

$\to$ $rarr$ If you are referring to perimeter, the scale factor would be 12.

Example:
Perimeter = $15$ $15$ $c m$ $cm$
Dilated by scale factor $4 = 60$ $4 = 60$ $c m$ $cm$
Dilated by scale factor $3 = 180$ $3 = 180$ $c m$ $cm$

To get from $15$ $15$ $c m$ $cm$ to $180$ $180$ $c m$ $cm$ , you would use a scale factor of $180 \div 15 = 12$ $180-:15=12$ .
The scale factor is equal to the change in perimeter between the smaller and dilated triangle.
For example, $5$ $5$ $c m$ $cm$ $\cdot$ $*$ $12$ $12$ $c m = 180$ $cm=180$ $c m$ $cm$

$\to$ $rarr$ If you are referring to area, the scale factor would also be 12.

Example:
Area = $4 \sqrt{3}$ $4sqrt(3)$ $c m^{2}$ $cm^2$
Dilated by scale factor $4 \approx 110.85$ $4 ~~ 110.85$ $c m^{2}$ $cm^2$
Dilated by scale factor $3 \approx 997.66$ $3 ~~ 997.66$ $c m^{2}$ $cm^2$

To get from $4 \sqrt{3}$ $4sqrt(3)$ $c m^{2}$ $cm^2$ to $997.66$ $997.66$ $c m^{2}$ $cm^2$ , you would use a scale factor of $\sqrt{997.66 \div 4 \sqrt{3}} \approx 12$ $sqrt(997.66-:4sqrt(3))~~12$
The only difference between the perimeter and area is that the change in area between two similar triangles is not equal to the scale factor.
For example, $4 \sqrt{3}$ $4sqrt(3)$ $c m$ $cm$ $\cdot$ $*$ $12$ $12$ $c m \neq 997.56$ $cm!=997.56$
To get the scale factor for the area between two triangles, you must square root the change in area between the triangles.

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A triangle is dilated using a scale factor of 4. The image is then dilated using a scale factor of 3. What scale factor could you use to dilate the original triangle to get the final image?

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Explanation:

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