Chapter 0.2, Problem 18E

a)

To determine

the expressions for the Monica’s new office.

Answer to Problem 18E

Expressions for dimensions of Monica’s new office is $\left(x+3\right)$ and $\left(x+5\right)$ .

Explanation of Solution

Given information:

It is given that Monica’s current office is in the shape of square. Her office in the company’s new building will be 3feet wider and 5 feet longer.

Let the length of the side of current office be x.

According to the question, her new office, will have

Length = $\left(x+3\right)$

Breadth = $\left(x+5\right)$

So,

Expressions for dimensions of Monica’s new office is $\left(x+3\right)$ and $\left(x+5\right)$ .

b)

To determine

the polynomial expression for the area of Monica’s new office.

Answer to Problem 18E

The expression after product of the length and breadth is $x^2+8x+15$ .

Explanation of Solution

Given information:

It is given that Monica’s current office is in the shape of square. Her office in the company’s new building will be 3feet wider and 5 feet longer.

According to the question, her new office, will have

Length = $\left(x+3\right)$

Breadth = $\left(x+5\right)$

So,

Expressions for polynomial expression for the area of Monica’s new office = $\left(x+3\right)\left(x+5\right)$ .

After simplifying it,

  $\begin{array}{c}\left(x+3\right)\left(x+5\right)=x\left(x+5\right)+3\left(x+5\right)\\ =x^2+5x+3x+15\\ =x^2+8x+15\end{array}$

c)

To determine

the value by how much it is large than previous office.

Answer to Problem 18E

The new office is 71 feet²is larger.

Explanation of Solution

Given information:

It is given that Monica’s current office is in the shape of square. Her office in the company’s new building will be 3feet wider and 5 feet longer.

According to the question, her new office, will have

Length = $\left(x+3\right)$

Breadth = $\left(x+5\right)$

So,

Expressions for polynomial expression for the area of Monica’s new office = $\left(x+3\right)\left(x+5\right)$ .

After simplifying it,

  $\begin{array}{c}\left(x+3\right)\left(x+5\right)=x\left(x+5\right)+3\left(x+5\right)\\ =x^2+5x+3x+15\\ =x^2+8x+15\end{array}$

Here, it is being asked to suppose Monica’s current office is 7 feet by 7 feet.

The area of current office is 49feet².

Now, finding the area of the Monica’s new office,

By putting x = 7,

  $\begin{array}{c}\left(x+3\right)\left(x+5\right)=\left(7+3\right)\left(7+5\right)\\ =10\times 12\\ =120fee{t}^2\end{array}$

So,

Difference in area =

  $120-49=71fee{t}^2$

So, the new office is 71 feet²is larger.