Chapter 3.4, Problem 29PPS

To determine

To construct: The set of inequalities that form a bounded region with an area of $20{\text{ units}}^2$ and lie only on fourth quadrant.

Answer to Problem 29PPS

The set of inequalities that form a bounded region with an area of $20{\text{ units}}^2$ and lie only on fourth quadrant is $-2\ge y\ge 6\text{ and }11\ge x\ge 6$.

Explanation of Solution

Given information:

The bounded region should have area $20{\text{ units}}^2$ and must lie in fourth quadrant.

Consider the inequalities $-2\ge y\ge 6\text{ and }11\ge x\ge 6$ . Plot them on coordinate plane.

  

It is observed that bounded region lies only in fourth quadrant. Vertices of common bounded region is $\left(6,-2\right),\left(11,-2\right),\left(11,-6\right)\text{ and }\left(6,-6\right)$.

It forms a rectangle whose length is 4 and width is 5.

It is known that area of rectangle is length multiplied by width.

For the provided inequalities, from the graph it is clear that area is $20{\text{ units}}^2$.

Thus, the set of inequalities that form a bounded region with an area of $20{\text{ units}}^2$ and lie only on fourth quadrant is $-2\ge y\ge 6\text{ and }11\ge x\ge 6$.