Question

question 23 of 50
the value of ad is
26.
27.
28.

Explanation:

Step1: Identify the theorem

Since \( BD \) is the angle bisector, and \( DA \perp AB \), \( DC \perp BC \), by the Angle - Bisector Theorem (a point on the angle bisector is equidistant from the two sides of the angle), we have \( AD = DC \).

Step2: Set up the equation

Given \( AD = 3x \) and \( DC=2x + 9 \), so we set up the equation \( 3x=2x + 9 \).

Step3: Solve for \( x \)

Subtract \( 2x \) from both sides of the equation \( 3x=2x + 9 \). We get \( 3x-2x=2x + 9-2x \), which simplifies to \( x = 9 \).

Step4: Calculate the length of \( AD \)

Substitute \( x = 9 \) into the expression for \( AD \), which is \( 3x \). So \( AD=3\times9 = 27 \).

Answer:

27