Question

From the triangle below, if AD = 5 and CD = 20, find the length of side BD.

Answer 1

The length of side BD, given that AD = 5 and CD = 20 is 10 (Option A)

Data obtained from the question

• Length of side AD = 5
• Length of side CD = 20
• Length of side BD =?

How to determine the length of side BD

Since the triangles are similar, we can obtain the length of side BD as illustrated below:

CD / BD = BD / AD

20 / BD = BD / 5

Cross multiply

BD × BD = 20 × 5

BD² = 100

Take the square root of both sides

BD = √100

BD = 10

Thus, the length of side BD is 10

Learn more about similar triangles:

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Answer 2

Answer: 10

Step-by-step explanation:

By the geometric mean theorem,

$\frac{BD}{5}=\frac{20}{BD}\\\\(BD)^2 = 100\\\\BD=10$