Chapter 11.9, Problem 16PPS

To determine

Tofind:the perimeter of the celling which is modeling as shown. Round up to nearest tenth.

Answer to Problem 16PPS

  $78.49\text{ft}$ .

Explanation of Solution

Given:

Thegiven figure is

  

Calculation:

According to the given figure is perimeter in the question,

The five sides are known $23\text{ft,12ft,}7\text{ft,10ft,and}18\text{ft}$ .

Now, to find the perimeter of the sixth sides of the figure.

The base of the triangle is $\left(23-10-7\right)ft$ i.e. 6 ft and its height is $\left(18-12\right)ft$ i.e. 6 ft.

Now use Pythagoras theorem to find third side.

Let the third side be x.

Therefore,

  $\begin{array}{l}{x}^2=6^2+6^2\\ =36+36=72\\ \therefore x=\sqrt{72}\approx 8.49\end{array}$ .

Thus, the perimeter of the figure is sum of its sixth side.

  $\begin{array}{l}P=23ft+12ft+7ft+8.49ft+10ft+18ft\\ P=78.49\end{array}$ .

Hence, theamount of modeling required is $78.49\text{ft}$ .