Question

EF is parallel to BC. If ED is 9.6, BE is 8, and EF is 12. Find the length of BC

Answer 1

To determine the length of BC, we use the similarity of triangles principle, setting up a proportion between line segments EF and ED, which are proportional to BC and BE respectively. After cross multiplying and solving for BC, we find that BC is 10 units long.

Step-by-step explanation:

The question involves finding the length of line segment BC given that line segments EF and BC are parallel and other lengths in the figure are provided.

Since EF is parallel to BC, and we know the lengths of ED, BE, and EF, we can say that the ratio of EF to ED should be the same as the ratio of BC to BE because they would form similar triangles.

Therefore, we can use a proportion to find the length of BC as follows:

1. Write down the known lengths: ED = 9.6, BE = 8, EF = 12.
2. Set up the proportion using the similarity of triangles: EF/ED = BC/BE.
3. Plug in the known values: 12/9.6 = BC/8.
4. Cross multiply and solve for BC: BC = (12/9.6) * 8.
5. Calculate BC: BC = 1.25 * 8 = 10.

The length of BC is 10 units.