Given:
• AD = 3
,
• DC = 27
,
• BD = x + 3
Let's solve for x.
To solve for x, apply the altitude formula:
[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]
Where BD is the altitude.
Cross multiply:
[tex]BD^2=AD*DC[/tex]
Plug in the values and solve for x:
[tex]\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}[/tex]
Take the square root of both sides:
[tex]\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}[/tex]
Therefore, the value of x is 6 .
ANSWER:
d. 6
