A square patio is surronded by a brick walkway. What is the total area of the patio AND the walkway? The patio is 5 ft x 5 ft
(x^2+15x+50) sq. ft
(x^2+20x+100) sq. ft
(x^2+10x+25) sq ft
(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 and the area of the walkway.
The patio area is the area of a square with side length 5 ft, which is 5 ft * 5 ft = 25 sq ft.
The walkway surrounds the patio on all sides, which means it is the same width on all sides. Let's call this width "x".
To find the area of the walkway, we need to take the difference between the total area of the outer square and the area of the inner square (the patio).
The total area of the outer square is (5 + 2x) ft * (5 + 2x) ft = (25 + 20x + 4x^2) sq ft.
The area of the inner square (the patio) is 5 ft * 5 ft = 25 sq ft.
So, the area of the walkway is (25 + 20x + 4x^2) sq ft - 25 sq ft = 20x + 4x^2 sq ft.
Therefore, the total area of the patio and the walkway is the sum of the patio area and the walkway area:
Total area = patio area + walkway area
= 25 sq ft + (20x + 4x^2) sq ft
= 4x^2 + 20x + 25 sq ft
The correct answer is therefore:
(x^2 + 20x + 25) sq ft