Question

What is BD? (geometry

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The length of BD = 8cm from triangle ABC when BD is the bisecting line of AC. The length of AD = 4cm and DC = 16cm.

Given that,

In the figure we have the triangle ABC.

BD is the bisecting line of AC.

The length of AD = 4cm and DC = 16cm

We have to find the length of BD.

We know that,

To find ∠A

In ΔABD,

cosA = $\frac{AD}{AB}$  

cosA = $\frac{4}{AB}$ ----------->equation(1)

In ΔABC,

cosA = $\frac{AB}{AC}$  

cosA = $\frac{AB}{20}$ ----------->equation(2)

From equation(1) and equation(2)

$\frac{4}{AB}$ = $\frac{AB}{20}$

AB² = 80

Taking square root on both sides,

AB = 4√5

From ΔABD

BD² = AB²-AD²

BD² = 80 - 16

BD² = 64

Taking square root on both sides

BD = 8

Therefore, The length of BD = 8cm.

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