Chapter 8.1, Problem 8PSA

a

To determine

To calculate:The ratio of perimeters of two given squares.

Answer to Problem 8PSA

The ratio of perimeters of two given squares is $\frac{5}{7}$

Explanation of Solution

Given information Two squares with sides 5 units and 7 units

Formula used Perimeter of a square

= $4\times \text{ measure of one side}$

Calculation Perimeter of a square of side 5 units

= $4\times \text{ measure of one side}$

  $\begin{array}{l}=4\times 5\\ =20\text{ units}\end{array}$

Perimeter of a square of side 7 units

= $4\times \text{ measure of one side}$

  $\begin{array}{l}=4\times 7\\ =28\text{units}\end{array}$

Ratios of perimeters

  $\begin{array}{l}=\frac{20}{28}\\ =\frac{5}{7}\end{array}$

b

To determine

To calculate:The ratio of areas of two given squares.

Answer to Problem 8PSA

The ratio of areas of two given squares is 25 : 49

Explanation of Solution

Given information Two squares with sides 5 units and 7 units

Formula used Area of a square

= ${\left(\text{measure of one side}\right)}^2$

Calculation Area of a square of side 5 units

= ${\left(\text{measure of one side}\right)}^2$

  $\begin{array}{l}=5^2\\ =25\text{ units}\end{array}$

Area of a square of side 7 units

= ${\left(\text{measure of one side}\right)}^2$

  $\begin{array}{l}=7^2\\ =49\text{units}\end{array}$

Ratios of perimeters

= 25 : 49