Question

find the value of the variable.
16.5
11
29
p
p =

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments of lengths \(a\) and \(b\), and the other two sides of the triangle have lengths \(c\) and \(d\), then \(\frac{a}{b}=\frac{c}{d}\).
Let the length of the segment adjacent to \(p\) be \(x = 29 - 11=18\). According to the Angle - Bisector Theorem, \(\frac{11}{18}=\frac{16.5}{p}\).

Step2: Cross - multiply to solve for \(p\)

Cross - multiplying gives \(11p=16.5\times18\).
First, calculate \(16.5\times18=(16 + 0.5)\times18=16\times18+0.5\times18=288 + 9 = 297\).
Then, solve for \(p\) from \(11p = 297\). Divide both sides by 11: \(p=\frac{297}{11}\).

Step3: Perform the division

\(p = 27\).

Answer:

\(27\)