Final answer:
The student's question involves comparing the side lengths of two triangles using proportions. By setting the given scale to actual size ratios equal to one another for length and width, one can find the unknown scale lengths or actual lengths as needed.
Step-by-step explanation:
The student is asking to find the ratio of the side lengths of Δa'b'c' to the corresponding side lengths of Δa'1b'1c'1. To solve this, we can use proportions, which can help us establish a relationship between the side lengths of the two triangles.
If we have a scale to actual size ratio of 1/20 for one triangle and a scale to actual size ratio of 1/5.5 for another, we can compare these two by setting up a proportion:
scale/actual = 1/20
scale/actual = 1/5.5
We can write two proportions by setting the two length ratios equal to one another and two width ratios equal to one another. For example:
Length ratio: 1/50 = 0.5/5
Width ratio: w/30 = 0.5/
Using these proportions, we can solve for the unknown scale lengths of the sides or the actual lengths, depending on what is required.