ANSWER THIS CORRECTLY.
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 correct answer is C. (x^2 + 25x + 125) sq.ft.
To find the total area of the patio and the walkway, we need to add the area of the patio to the area of the walkway.
The area of the patio is the area of the square, which is (5ft)(5ft) = 25 sq.ft.
The walkway surrounds the patio on all four sides, so we need to add the width of the walkway on each side.
The width of the walkway is x ft on the bottom and x ft on the right side, so the total width of the walkway is 2x ft.
The length of the walkway is the same as the length of the patio, which is 5 ft.
The total area of the walkway is then (2x ft)(5 ft) = 10x sq.ft.
Therefore, the total area of the patio and the walkway is (25 sq.ft + 10x sq.ft) = 25 + 10x sq.ft.
Simplifying, we get x^2 + 25x + 125 sq.ft, which is option C.