A square patio is surrounded by a brick walkway. What is the total area of the patio AND the walkway?
Dimensions on each side of the square: 5ft
The bottom of the square: x ft
The right side of the square: x ft
A. (x^2 + 20x + 100) sq.ft
B. (x^2 + 15x + 50) sq.ft
C. (x^2 + 25x + 125) sq.ft
D. (x^2 + 10x + 25) sq.ft
The area of the patio is given by the formula A = side^2, where side is the length of one side of the square. In this case, the side is 5ft, so the area of the patio is 5^2 = 25 sq.ft.
The walkway surrounds the patio on all sides. Since the dimensions of the patio are the same on each side (5ft), the width of the walkway is given by the equation x - 5 - 5 = x - 10.
The total area of the patio and the walkway is equal to the area of the patio plus the area of the walkway. The area of the walkway is given by the equation (x - 10)^2. Therefore, the total area is given by the equation:
Total area = Patio area + Walkway area
Total area = 25 + (x - 10)^2
Total area = 25 + x^2 - 20x + 100
Total area = x^2 - 20x + 125 sq.ft
Therefore, the total area of the patio and the walkway is (x^2 - 20x + 125) sq.ft.
The correct answer is C. (x^2 + 25x + 125) sq.ft.