Chapter 5.7, Problem 33E

(a)

To determine

To write: a system of linear inequalities represented by the shaded rectangle.

Answer to Problem 33E

The system of inequalities is $x\ge -1,x\le 6,y\ge -3\text{and}y\le 1$.

Explanation of Solution

Given information:

The following points are the vertices of a shaded rectangle

  $\left(-1,1\right),\left(6,1\right),\left(6,-3\right),\left(-1,-3\right)$

Calculation:

The two vertical lines of the rectangle are passing through $x$ points of $-1$ and 6. It means the inequalities for the vertical boundaries are

  $x\ge -1$ and $x\le 6$

The two horizontal lines of the rectangle are passing through $y$ points $-3$ and 1. It means the inequalities for the horizontal boundaries are

  $y\ge -3$ and $y\le 1$

Therefore, the system of inequalities is $x\ge -1,x\le 6,y\ge -3\text{and}y\le 1$.

(b)

To determine

To find: the area of the rectangle.

Answer to Problem 33E

The area of the rectangle is $28$ square units.

Explanation of Solution

Calculation:

The length of the rectangle along horizontal direction is difference between $x$ points of $-1$ and 6 which is 7 units.

The length of the rectangle along vertical direction is difference between $y$ points of $-3$ and 1 which is 4 units.

The area of the rectangle is $7\times 4=28$ square units.

Therefore, the area of the rectangle is $28$ square units.