Chapter 6, Problem 36SGR

To determine

The length of CE.

Answer to Problem 36SGR

  $CE=7.9$

Explanation of Solution

Given:

ABCD is a rhombus.

  $EB=9,AB=12\text{ and m}\angle ABD=55.$

Calculation:

According to the Theorem of Diagonals of a Rhombus;

As the given figure is a rhombus, its diagonals are perpendicular.

Therefore,

  $\angle AEB$ is a right angle and hence, triangle AEB is a right triangle.

So,

  $\begin{array}{l}AE=\sqrt{{\left(AB\right)}^2-{\left(EB\right)}^2}\\ AE=\sqrt{{\left(12\right)}^2-{\left(9\right)}^2}\\ AE=\sqrt{63}\\ AE\approx 7.9\end{array}$

The diagonals of a rhombus bisect each other, therefore;

  $\overline{CE}\cong \overline{AE}$

So, length of CE will be:

  $\begin{array}{l}CE=AE\\ CE=7.9\end{array}$