Chapter 6, Problem 34SGR

To determine

The length of AE.

Answer to Problem 34SGR

  $AE\approx 7.9$

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,

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