# Given two similar triangles with a scale factor of a : b, show the ratio of their perimeters is also a : b?

Thus the ratio of the perimeters is the same as the ratio of the sides, that is, of the scale factor between the triangles.

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Given two similar triangles with a scale factor of ( \frac{a}{b} ), the ratio of their perimeters is also ( \frac{a}{b} ).

Let's denote the lengths of corresponding sides in the two similar triangles as follows:

( a_1 ) and ( a_2 ) for the corresponding sides in the first and second triangles, respectively.

( b_1 ) and ( b_2 ) for the other pair of corresponding sides.

The perimeters of the two triangles are ( P_1 ) and ( P_2 ) respectively.

The scale factor between the two triangles is ( \frac{a}{b} ).

By definition, the scale factor ( \frac{a}{b} ) is:

[ \frac{a_2}{a_1} = \frac{b_2}{b_1} = \frac{P_2}{P_1} ]

Therefore, the ratio of their perimeters is ( \frac{P_2}{P_1} = \frac{a_2}{a_1} = \frac{b_2}{b_1} = \frac{a}{b} ).

Hence, the ratio of their perimeters is also ( \frac{a}{b} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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