Chapter 8.4, Problem 39PPS

(a)

To determine

The area of two squares.

Explanation of Solution

The solution for the given statement can be obtained as:

  

The area of the square is side square. Therefore,

Area of larger square = $a^2$

Area of smaller square = $b^2$

(b)

To determine

The area of the remaining region.

Explanation of Solution

The solution for the given statement can be obtained as:

  

The area of the remaining region will be:

  $a^2–b^2$

(c)

To determine

The value of dimensions.

Explanation of Solution

The solution for the given statement can be obtained as:

  

Width = a − b

Length = a + b

(d)

To determine

The area of the rectangle.

Explanation of Solution

The solution for the given statement can be obtained as:

  $\begin{array}{c}A=l\times w\\ =(a+b)(a-b)\end{array}$

(e)

To determine

The complete statement.

Explanation of Solution

The rectangle having sides a-b and a + b have same area as the area of the figure $a^2-b^2$

  $\text{so }{a}^2-b^2=\left(a-b\right)\left(a+b\right).$