Chapter 4, Problem 28CCSR

Solution

To find: what is an expression that represents the area of the new flower bed?

Expression for new area of flowerbed is $2w^2+5w-3{\text{ feet}}^2$ .

Given: original width of rectangular flowerbed $w$ , in feet.

Concept Used:

Area of rectangle is $\text{length}\times \text{width}$ .

Calculation:

Original width of rectangular flowerbed $w$ , in feet.

She increased the width by 3 feet:

New width is $w+3\text{ feet}$ .

Now, length is 1 foot less than twice the original width:

New length is $2w-1\text{ feet}\text{.}$

Area of rectangular new flowerbed $=\left(2w-1\right)\times \left(w+3\right)$ .

Simplifying the expression:

  $\begin{array}{c}\text{Area of rectangular new flowerbed}=\left(2w-1\right)\times \left(w+3\right)\\ =2w\left(w+3\right)-1\left(w+3\right)\\ =2w^2+6w-w-3\\ =2w^2+5w-3\end{array}$

Conclusion:

Expression for new area of flowerbed is $2w^2+5w-3{\text{ feet}}^2$ .