Chapter 4.5, Problem 21PPE

To determine

To find : a function rule for area of the rectangle and the area of the rectangle when its width is 2 ft.

Answer to Problem 21PPE

The function rule for the area of the triangle is

Area= $3w^2-2w$

where w is width of the rectangle in feet.

Area of the rectangle when its width is 2 ft is 8 square ft.

Explanation of Solution

Given information: The length of a rectangle is 2 ft less than three times its width.

Calculation:

Let the length and width (in ft) of the rectangle be l and w respectively.

Since, length of the rectangle is 2 ft less than three times its width , so $l=3w-2$ .

Now, area of the rectangle is

Area=length $\times$ width

Area= $\left(3w-2\right)w$

Area= $3w^2-2w$ square ft.

Thus, function rule for the area of the triangle is

Area= $3w^2-2w$

where w is width of the rectangle in feet.

Now, area of the rectangle when its width is 2 ft is

Area $=3{\left(2\right)}^2-2\left(2\right)=12-4=8$ square feet.