Point C on line segment BD. Given BD = 5x, BC = 4x, and CD = 4, determine the numerical length of BD.

The numerical length of BD is 20 units

Step-by-step explanation:

Let us solve the question

∵ Point C lies on the line segment BD

→ That means C divides BD into 2 parts

∴ C divides BD into 2 parts BC and CD

∴ BD = BC + CD

∵ BD = 5x

∵ BC = 4x

∵ CD = 4

→ Substitute them in the equation above

∴ 5x = 4x + 4

→ Subtract 4x from both sides

∵ 5x - 4x = 4x - 4x + 4

∴ x = 4

→ Substitute the value of x in the expression of BD

∵ BD = 5x

∵ x = 4

∴ BD = 5(4) = 20

∴ The numerical length of BD is 20 units