Chapter 8.3, Problem 48HP

To determine

To calculate:

The perimeter of given quadrilateral $ABCD$ .

Answer to Problem 48HP

The perimeter of given quadrilateral $ABCD$ is $59.8units.$

Explanation of Solution

Given information:

Quadrilateral $ABCD$ :

  

Calculation:

The given campsite figure of two congruent isosceles right triangles and a rectangle.

Theorem of $45°-45°-90°$ triangle shows that

  $\begin{array}{l}AB=CD\\ =\sqrt{2}\left(FC\right)\\ =\sqrt{2}\left(7\right)\\ =7\sqrt{2}\end{array}$

Properties, of rectangle show that

  $\begin{array}{l}BC=EF\\ =AD-AE-FD\\ =AD-2\left(FC\right)\\ =27-2\left(7\right)\end{array}$

Find, the perimeter of the quadrilateral $ABCD$ .

  $\begin{array}{l}P=AB+BC+CD+AD\\ =7\sqrt{2}+13+7\sqrt{2}+27\\ =40+14\sqrt{2}\\ =59.8\end{array}$

Hence, the perimeter is $40+14\sqrt{2}\approx 59.8units.$