Chapter SH, Problem 6.17EP

a.

To determine

Find the exact perimeter of the given shape.

Answer to Problem 6.17EP

The perimeter of the given shape is $19.799$ .

Explanation of Solution

Given:

The given shape is

  

Calculation:

The given shape is a rectangle.

Perimeter of the rectangle $=2\left(\text{length}+\text{width}\right)$

Length $=\sqrt{32}$

Width $=\sqrt{18}$

Perimeter $=2\left(\sqrt{32}+\sqrt{18}\right)$

  $\begin{array}{l}=2\left(\sqrt{2\cdot 16}+\sqrt{2\cdot 9}\right)\\ =2\left(\sqrt{2\cdot 4^2}+\sqrt{2\cdot 3^2}\right)\\ =2\left(4\sqrt{2}+3\sqrt{2}\right)\\ =2\cdot 7\sqrt{2}\\ =14\cdot \sqrt{2}\\ =19.799\end{array}$

Hence the perimeter of the given shape is $19.799$ .

b.

To determine

Find the exact circumference of the given shape.

Answer to Problem 6.17EP

The circumference of the given shape is $43.509$ .

Explanation of Solution

Given:

The given shape is

  

Calculation:

The given shape is a circle.

Circumference of the circle $=2\pi r$

Radius $r=\sqrt{48}$

Circumference $=2\pi \sqrt{48}$

  $\begin{array}{l}=2\cdot 3.14\cdot \sqrt{3\cdot 16}\\ =6.28\cdot \sqrt{3\cdot 4^2}\\ =6.28\cdot 4\sqrt{3}\\ =25.12\sqrt{3}\\ =43.509\end{array}$

Hence the circumference of the given shape is $43.509$ .