You are buying a fence to enclose a garden
that has an area of 360 square feet.
x + 9 The bottom of garden
x side of garden
a) What is the width of the area to be
enclosed?
Answer in units of ft
b) How much fencing do you need?
Answer in units of ft
x(x+9) = 360
x^2 + 9x - 360 = 0
360 = 5 * 2 * 3 * 3 * 2 * 2
Find combination of factors that will give you 9.
To find the width of the area to be enclosed, we can use the formula for the area of a rectangle, which is length times width. In this case, we know that the area of the garden is 360 square feet and the length is given by x + 9. Therefore, we can set up the equation:
(x + 9) * width = 360
To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by (x + 9):
width = (360 / (x + 9))
So, the width of the area to be enclosed is (360 / (x + 9)) ft.
To find the amount of fencing needed, we need to calculate the perimeter of the enclosed area. The perimeter is the sum of all the sides of the garden. In this case, we have two sides with length x, and two sides with length (x + 9). Therefore, the perimeter is given by:
perimeter = 2(x) + 2(x + 9)
Simplifying this expression gives:
perimeter = 2x + 2x + 18
perimeter = 4x + 18
So, the amount of fencing needed is 4x + 18 ft.