Question

In triangle ABC, DEAC. If AD=12, BD=3, and CE=10, find BE.

Answer 1

Using the Triangle Proportionality Theorem and properties of similar triangles, we calculated the length of BE in triangle ABC to be 12.5 units.

Step-by-step explanation:

The question appears to be related to the topic of triangle proportionality in geometry, which is a high school level mathematics concept. Given that DE is parallel to AC in △ABC, and the lengths AD = 12, BD = 3, and CE = 10 are provided, we can find BE using the properties of similar triangles. By the Triangle Proportionality Theorem, the segments are proportional, so we can set up the proportion AD / AB = CE / BE, where AB is the sum of AD and BD (AB = AD + BD = 12 + 3 = 15). Substituting the known values into the proportion gives us 12 / 15 = 10 / BE. After cross-multiplication, BE can be solved as BE = (10 × 15) / 12. This simplifies to BE = 150 / 12, which further simplifies to BE = 12.5. Therefore, the length of BE is 12.5 units.

Answer 2

BE = 2.5

Step-by-step explanation:

Remark

Use triangles ABC and DEB.

Formula

AB/DB = BC / BE

Givens

• AB = 15
• BD = 3
• BC = 10 + x
• BE = x

Solution

15/3 = (10 + x)/x Cross multiply

15x = 3(10 + x) Remove the brackets

15x = 30 + 3x Subtract 3x from both sides.

15x - 3x = 30 Combine

12x = 30 Divide by 12

x = 30/12

x = 2.5