Chapter 5.7, Problem 29PSC

a.

To determine

To find: An expression to represent the shaded area.

Answer to Problem 29PSC

  $\text{Area of the shaded region}=324-x^2$ .

Explanation of Solution

Given information:

A figure is given as below.

  

Calculation:

A figure is given as below.

  

From above figure,

  $\begin{array}{l}\text{Area of the shaded region}=\text{Area of complete rectangle}-\text{Area of unshaded square}\\ \Rightarrow \text{Area of the shaded region}=\left(12\times 27\right)-\left(x\times x\right)\\ \Rightarrow \text{Area of the shaded region}=324-x^2\end{array}$

Hence, expression for representing area of shaded region would be $324-x^2$ .

b.

To determine

To find: An inequality that given area of square.

Answer to Problem 29PSC

Area of square would be given as $x^2;0<x\le 12$ .

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

A figure is given as below.

  

From above figure,

  $\begin{array}{l}\text{Area of unshaded square}=x^2\\ \text{Length of square can be maximum upto width of rectangle}\text{.}\\ \text{i}\text{.e}\text{. }0<x\le 12\end{array}$

Hence, area of square would be given as $x^2;0<x\le 12$ .