Question

Triangle ABC is similar to triangle AEF.

Given:
AB = 48 millimeters
BC = 36 millimeters
AC = x millimeters
EF = 12 millimeters
Find:
x (in millimeters)

1. 16 millimeters
2. 24 millimeters
3. 32 millimeters
4. 40 millimeters

Answer 1

The length of side AC in triangle ABC is found by setting up a proportion using the corresponding sides of the similar triangles ABC and AEF. The calculated length of AC is 48 millimeters, which indicates a discrepancy with the provided options.

Step-by-step explanation:

The student has asked to find the length of side AC in millimeters for triangle ABC, which is similar to triangle AEF. Since the triangles are similar, the sides are proportional. We are given that AB is 48 millimeters, BC is 36 millimeters, and EF is 12 millimeters. To find x, which is the length of AC, we can set up a proportion with the corresponding sides of the triangles:

AB/EF = AC/EF

By substituting the known values we get:

48/12 = x/12

By cross-multiplying, we find that:

48 * 12 = x * 12

Therefore, x = 48. Since x represents the length of side AC, the answer is that AC is 48 millimeters.

Looking at the options provided by the student, it seems there might be a typo as none of the options match the calculated length. The correct length should be double-checked for accuracy.