Question

DE II AC. What equation can you use to find the length of CD?

Select the correct proportion for CD's length:
a) 4:x = 3:2
b) 4:2 = 3:x
c) 2:4 = x:3
d) 2 : x = 3:2

Answer 1

To find the length of CD, we must use the properties of similar triangles. The correct proportion, given the parallel lines and similarity of triangles, is 4:2 = 3:x where x represents the length of CD.

Step-by-step explanation:

The question asks for the appropriate proportion to use in order to find the length of CD given that DE is parallel to AC. Based on the context, it sounds like a question related to similar triangles or proportional parts within triangles.

We can use the properties of similar triangles to write the proportion correctly. Since DE is parallel to AC, triangle CDE is similar to triangle CAB by AA (Angle-Angle) similarity. Therefore, the ratios of corresponding sides are equal. If the lengths of DE and AC are in the proportion 4:2 (or reduced to 2:1), and the lengths of CE and AB are in the proportion 3:x, then the proportions should match. Thus, we get that the proportion b) 4:2 = 3:x is the correct one to find CD's length.