Chapter 6.5, Problem 23PPS

To determine

The length of AP.

Answer to Problem 23PPS

  $AP=9$

Explanation of Solution

Given:

ABCD is a rhombus.

  $PB=12,AB=15\text{ and m}\angle \text{ABD = 24}\text{.}$

Calculation:

According to Rhombi Theorem, if the diagonals of a parallelogram are perpendicular, then it is a rhombus.

The measure of angle APB is a right-angle, hence, triangle APB is a right triangle.

Consider the triangle APB:

  $\begin{array}{l}AP=\sqrt{{\left(AB\right)}^2-{\left(PB\right)}^2}\\ AP=\sqrt{{\left(15\right)}^2-{\left(12\right)}^2}\\ AP=\sqrt{81}\\ AP=9\end{array}$