Question

question 46 of 50
the value of x is:
diagram with triangle, right angles at a and c, bd as angle bisector, ad = 3x, cd = 2x + 9
options: 9, 18, 27

Explanation:

Step1: Identify the theorem

Since \( BA \perp AD \) and \( BC \perp CD \), and \( BD \) is the angle bisector (as the two angles at \( B \) are marked equal), by the Angle - Bisector Theorem for perpendicular distances, the distances from a point on the angle bisector to the two sides of the angle are equal. So \( AD = CD \).

Step2: Set up the equation

We know that \( AD = 3x \) and \( CD=2x + 9 \). So we set up the equation \( 3x=2x + 9 \).

Step3: Solve for \( x \)

Subtract \( 2x \) from both sides of the equation \( 3x=2x + 9 \).
\( 3x-2x=2x + 9-2x \)
\( x = 9 \)

Answer:

\( 9 \)