Question

A square plot of land will be fully used for a square flower bed with a 3-foot-wide walkway around it. The area of the entire plot, including the walkway, is P square feet. Which expression gives the length of the flower bed?

a) (√(P + 9))
b) (√(P - 9))
c) (√(P) + 3)
d) (√(P) - 3)

Answer 1

The length of the flower bed is given by expression d) √(P) - 3, representing the side of the square flower bed minus the width of the walkway on one side.

Step-by-step explanation:

The question involves finding the expression for the length of the flower bed that is surrounded by a 3-foot-wide walkway, given the area of the entire plot (including the walkway) is P square feet. Let's denote the side of the flower bed as f. Including the walkway, each side of the plot would be f + 2 × 3 feet because the walkway is 3 feet wide on both sides. Therefore, the area of the entire plot is ((f + 6)^2 = P). To find the length of the flower bed, we need to solve for f, which is f = √(P) - 6. Since f corresponds to the side length of the square flower bed, the correct expression is d) √(P) - 3, because the question asks for one side and not the entire width including both walkways.