Chapter 7.1, Problem 29WE

(a)

To determine

To find: The ratio of the perimeter of two square.

Answer to Problem 29WE

The required ratio is $3:5$ .

Explanation of Solution

Given:

The side of the first square is $60\text{cm}$ .

The side of the second square is $1\text{m}$

Calculation:

The perimeter of the square is,

  $P=4a$

Then, the perimeter of the first square is,

  $\begin{array}{c}P=4\left(60\text{cm}\right)\\ =240\text{cm}\end{array}$

The perimeter of the second square is,

  $\begin{array}{c}P=4\left(1\text{m}\right)\\ =4\text{m}\\ =400\text{cm}\end{array}$

Thus, the ratio of the perimeter is,

  $\frac{240\text{cm}}{400\text{cm}}=3:5$

(b)

To determine

To find: The ratio of the areaof two square.

Answer to Problem 29WE

The required ratio is $9:400$ .

Explanation of Solution

Given:

The side of the first square is $60\text{cm}$ .

The side of the second square is $1\text{m}$

Calculation:

The area of the square is,

  $A=a^2$

Then, the area of the first square is,

  $\begin{array}{c}A={\left(60\text{cm}\right)}^2\\ =3600{\text{cm}}^2\end{array}$

The area of the second square is,

  $\begin{array}{c}A={\left(100\text{cm}\right)}^2\\ =10000{\text{cm}}^2\end{array}$

Thus, the ratio of the area is,

  $\begin{array}{c}\frac{3600{\text{cm}}^2}{10000{\text{cm}}^2}=9{\text{cm}}^2:400{\text{cm}}^2\\ =9:400\end{array}$