Question

A concrete driveway is 5 feet longer than twice its width. It has a brick walkway 3 feet wide on the front and side of the driveway. The area of the brick walkway is 213
square feet. Find the dimensions of the driveway.​

Answer 1

Answer:

The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers

Step-by-step explanation:

Notice that the length "L" of the driveway can be written in terms of its width as:

L = 2 w + 5

based on the given information.

Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:

1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway

and the other one:

2) w + 3 times 3

Therefore the total area of the brick walkway is given by the formula:

(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet

Now we can solve for "w" in the above equation:

6 w + 15 + 3 w + 9 = 213

9 w + 24 = 213

9 w = 213 - 24

9 w = 189

w = 189/9

w = 21 feet

We can now solve for the L of the driveway, using the first formula we created:

L = 2 w + 5

L = 2 (21) + 5

L = 42 + 5

L = 47 feet

Therefore the driveway's width is w = 21 feet

and its length is L = 47 feet