A rectangular garden was planted measures 12 ft by 8 ft. You want to plant a border of roses around the garden of equal width with the same area as the garden. What should the width of the border of roses be?
the area of the garden is 96 ft^2
So, you want the walk of width w to also have 96 ft^2 of area. That means that
(12+2w)(8+2w) = 96+96
Now just solve for w.
To determine the width of the border of roses, we first need to find the area of the garden. The area of the garden can be calculated by multiplying its length by its width.
Given that the length of the garden is 12 ft and the width is 8 ft, we can calculate the area as follows:
Area of the garden = Length × Width
= 12 ft × 8 ft
= 96 square feet
Since we want the border of roses to have the same area as the garden, the area of the border of roses will also be 96 square feet.
Let's assume the width of the border of roses is x (in feet). Since the border is uniform on all sides of the garden, we can adjust the dimensions of the garden by adding 2x to its length and 2x to its width, resulting in a new length and width.
The new length of the garden including the border of roses will be: 12 ft + 2x
The new width of the garden including the border of roses will be: 8 ft + 2x
To find the area of the garden including the border, we multiply the adjusted length by the adjusted width:
Area of the garden + border = (12 ft + 2x) × (8 ft + 2x)
According to the problem, the area of the garden plus the border of roses is equal to 96 square feet. Therefore, we can write the equation as:
(12 ft + 2x) × (8 ft + 2x) = 96 square feet
We can now solve this equation to find the value of x, which will give us the width of the border of roses.