Solve the problem.
-Scot and Elizabeth recently built a rectangular garden measuring 40 feet by 50 feet. They want to add a paverstone walkway of uniform width around all sides of the garden. How wide can they make the walkway if
They purchased enough stones to cover 576 square feet?
A) 6 ft
B) 3 ft
C) 48 ft
D) 89 ft

Question

Quizplus · Accepted Answer

The area of the rectangular garden is given as 40 ft × 50 ft = 2000 sq ft. Let's say the width of the paverstone walkway is x, then the new dimensions of the garden will be (40+2x) ft by (50+2x) ft.

The area of the walkway will be (40+2x)(50+2x) - 40×50 = 576 sq ft.

Solving the above equation for x, we get x = 3 ft (after discarding the negative solution). Therefore, Scot and Elizabeth can make the walkway 3 feet wide. To find the width of the walkway, we need to subtract 2 times the width of the walkway from both the length and width of the garden:

Length of Garden with Walkway = 40 + 2w
Width of Garden with Walkway = 50 + 2w

The area of the walkway can then be expressed in terms of w:

Area of Walkway = (40 + 2w)(50 + 2w) - 40*50
Area of Walkway = 4w^2 + 180w

We know that the area of the walkway is 576 square feet, so we can set up the equation:

4w^2 + 180w = 576

Simplifying:

w^2 + 45w - 144 = 0

Using the quadratic formula, we get:

w = (-45 ± √(45^2 + 4*1*144))/2
w ≈ -48 or w ≈ 3

Since the width of the walkway can't be negative, we choose the positive root of w ≈ 3. Therefore, the maximum width of the walkway they can make is 3 feet.

Solve the Problem. -Scot and Elizabeth Recently Built a Rectangular Garden Measuring 40