Chapter 6.5, Problem 24PPS

To determine

The length of CP.

Answer to Problem 24PPS

  $CP=9$

Explanation of Solution

Given:

ABCD is a rhombus.

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

Calculation:

A rhombus has 4 congruent sides.

So,

  $\overline{BC}\cong \overline{AB,}$ therefore, BC = AB.

  $\begin{array}{l}BC=AB\\ BC=15\end{array}$

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

So, angle BPC is a right angle, and hence triangle BPC is a right triangle.

Therefore,

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