Chapter 11.5, Problem 16PPS

(a)

To determine

To find: The way in which the length of the side changes when the area is doubled.

Answer to Problem 16PPS

The case when the area is double then the side length is multiplied by $\sqrt{2}$ .

Explanation of Solution

Given:

The area of the polygon is $144{\text{m}}^2$ .

Calculation:

Consider the area of the polygon is $A$ and when the area is double the area is $2A$ .

Then, by the area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{2A}{A}\\ k=\sqrt{2}\end{array}$

Thus, the case when the area is double then the side length is multiplied by $\sqrt{2}$ .

(b)

To determine

To find: The way in which the length of the side changes when the area is doubled.

Answer to Problem 16PPS

The case when the area is tripled then the side length is multiplied by $\sqrt{3}$ .

Explanation of Solution

Given:

The area of the polygon is $144{\text{m}}^2$ .

Calculation:

Consider the area of the polygon is $A$ and when the area is tripled the area is $3A$ .

Then, by the area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{3A}{A}\\ k=\sqrt{3}\end{array}$

Thus, the case when the area is tripled then the side length is multiplied by $\sqrt{3}$ .

(c)

To determine

To find: The way in which the length of the side changes when the area is doubled.

Answer to Problem 16PPS

The case when the area is increased by factor $x$ then the side length is multiplied by $\sqrt{x}$ .

Explanation of Solution

Given:

The area of the polygon is $144{\text{m}}^2$ .

Calculation:

Consider the area of the polygon is $A$ and when the increased by factor $x$ then the area is $xA$ .

Then, by the area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{xA}{A}\\ k=\sqrt{x}\end{array}$

Thus, the case when the area is increased by factor $x$ then the side length is multiplied by $\sqrt{x}$ .