Chapter 6.1, Problem 47PPS

a.

To determine

To determine the length that should be cut to form the sides of the stage.

Answer to Problem 47PPS

Length is 6.5 feet.

Explanation of Solution

Given information :

Perimenter is 60 feet.

Length of the side is $\frac{\text{perimenter}}{\text{number of sides}}$

Hence length is $\frac{60}{8}=7.5$ feet.

b.

To determine

To determine the angle at which each board should be cut to fit.

Answer to Problem 47PPS

Angle should be ${67.5}^{\circ }$ .

Explanation of Solution

Given information :

Perimenter is 60 feet.

For an octagon formula for interior angle is,

$a=\frac{\left(n-2\right){180}^{\circ }}{n}$ wheren is the number of sides.

Hence each interior angle is $\frac{\left(8-2\right){180}^{\circ }}{8}={135}^{\circ }$ .

The table should be cut by the half the angle of the interior angle of the regular octagon.

Hence the required angle is $\frac{{135}^{\circ }}{2}={67.5}^{\circ }$ .