Question

From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

Answer 1

Given:

• AD = 3

,

• DC = 27

,

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

$\frac{AD}{BD}=\frac{BD}{DC}$

Where BD is the altitude.

Cross multiply:

$BD^2=AD*DC$

Plug in the values and solve for x:

$\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}$

Take the square root of both sides:

$\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}$

Therefore, the value of x is 6 .

ANSWER:

d. 6