Question

In the diagram below, BC connects points B and C on the congruent sides of isosceles triangle ADE, such that AABC is isosceles with vertex angle A.If AB=10; BD=5, and DE=12, what is the length of BC?

Answer 1

According to Thales Theorem, for this triangle, AB is to AD as BC is to DE.

Use this information to state a proportion and solve for BC.

Remember that AD is the sum of AB and BD:

$\begin{gathered} AD=AB+BD \\ AD=10+5 \\ AD=15 \end{gathered}$

Write the proportion:

$\frac{AB}{AD}=\frac{BC}{DE}$

Replace for the known values:

$\frac{10}{15}=\frac{BC}{12}$

Solve:

$\begin{gathered} BC=\frac{10}{15}\cdot12 \\ BC=8 \end{gathered}$

The length of BC is 8.