Find the area of the mulch border that surrounds the 5.5 ft by 8 ft flower garden. Show all work

Answer 1

To find the area of the mulch border, we need to first find the area of the entire garden including the border, and then subtract the area of the flower garden itself.

Area of the entire garden = (5.5 + 2x) * (8 + 2x), where x is the width of the mulch border.
Area of the flower garden = 5.5 * 8

Setting up the equations:

Area of the entire garden = (5.5 + 2x) * (8 + 2x)
= 44 + 16x + 11x + 4x^2
= 44 + 27x + 4x^2

Area of the flower garden = 5.5 * 8
= 44

Now, to find the area of the mulch border, we subtract the area of the flower garden from the area of the entire garden:

44 + 27x + 4x^2 - 44
= 27x + 4x^2

Now we know that the area of the mulch border is given by the equation 27x + 4x^2. However, we need to know x in order to calculate the exact area. Since x represents the width of the mulch border, the area is dependent on a specific value of x.