Question

The plan for a rectangular patio has a square garden centered in the patio with sides parallel to the sides of the patio. The patio is 20m long and 12m wide. If each side of the garden is "x" meters, the function, y= 240-x^2 gives the area of the patio in m^2. What values makes sense for the domain? Explain why

Answer 1

total area of patio = 240
area of garden = x^2
useable patio area = 12 - x^2

if x is more than 12, you can not walk around the garden

Answer 2

The width of 12 m governs the value of x
We must have
12 - 2x > 0
x < 6

the square garden must have sides less than 6 m each.