You are planning to build a walkway that surrounds a rectangular garden that is 10ft by 9ft. The width of the walkway around the garden is unknown, but it will be the same on every side.
a)what is the perimeter of the walkway along the outer edge ?
b) what is the combined area of the garden and the walkway ?
c)find the combined area when the width of the walkway is 4ft
garden:
length = 10 ft
width = 9 ft
garden including walkway:
length = 10+2x
width = 9+2x
a) perimeter = 2(10+2x) + 2(9+2x)
= 20 + 4x + 18 + 4x
= 8x + 38
b) area of whole thing
= (10+2x)(9+2x)
= 90 + 38x + 4x^2
c) when x=4
area according to formula = 90 + 38(4) + 4(4^2) = 306
area using arithmetic:
length = 18
width = 17
area = 18x17=306
The length of a rectangular rug is twice its width. The rug is centered in a rectangular room. Each edge is 3ft. From the nearest wall. What is the area of the room?
Didnt help
To find the answers, we need to follow these steps:
1. Visualize the problem: Draw a diagram of the garden and the walkway around it. This will help us understand the dimensions and relationships between different parts.
2. Define the variables: Let's define the width of the walkway as "w."
a) Perimeter of the walkway along the outer edge:
To find the perimeter, we need to calculate the length of each side of the outer edge.
- The length of the outer edge parallel to the length of the garden is (10ft + 2w).
- The length of the outer edge parallel to the width of the garden is (9ft + 2w).
Therefore, the perimeter of the walkway along the outer edge can be calculated as:
P = 2(10ft + 2w) + 2(9ft + 2w) = 20ft + 4w + 18ft + 4w
P = 38ft + 8w
b) Combined area of the garden and the walkway:
To find the combined area, we need to calculate the area of the garden and add it to the area of the walkway.
- The area of the garden is given by the length multiplied by the width, which is 10ft * 9ft = 90ft².
- The area of the walkway is given by the total area of the outer edge minus the area of the garden. Since the walkway has a uniform width on all sides, the length and width of the walkway rectangle will be (10ft + 2w) and (9ft + 2w) respectively.
Therefore, the area of the walkway can be calculated as:
A_w = (10ft + 2w) * (9ft + 2w)
The combined area of the garden and the walkway is given by:
A_combined = A_garden + A_w
c) Find the combined area when the width of the walkway is 4ft:
Using the formula from part b, substitute w = 4ft into the equation to calculate the combined area.
A_combined = A_garden + (10ft + 2(4ft)) * (9ft + 2(4ft))
Simplify and solve the equation to get the final answer.