# Suppose you have triangle ABC with AB = 5, BC = 7, and CA = 10, and also triangle EFG with EF = 900, FG = 1260, and GE = 1800. Are these triangles similar, and if so, what is the scale factor?

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Yes, these triangles are similar. The scale factor between the two triangles can be found by comparing the ratios of corresponding side lengths.

For triangle ABC, the ratio of side lengths AB to EF, BC to FG, and CA to GE are:

AB/EF = 5/900, BC/FG = 7/1260, CA/GE = 10/1800.

Simplifying these ratios, we find:

AB/EF = 1/180, BC/FG = 1/180, CA/GE = 1/180.

Since all corresponding side ratios are equal, the triangles are similar, and the scale factor is 1/180.

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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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