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 total area of the patio AND the walkway can be calculated by adding the area of the patio and the area of the walkway separately.
The area of the patio is equal to the side length of the square squared, which is (5ft)^2 = 25 sq.ft.
The walkway surrounds the patio, so the dimensions of the walkway will be the same as the dimensions of the patio, plus some extra space added on all four sides.
On each side of the square, there is a walkway of width x feet. Since there are four sides, the total width of the walkway will be 4x feet.
Therefore, the total area of the walkway is equal to the length of the patio plus the extra width of the walkway, multiplied by the width of the walkway.
Area of the walkway = (5ft + 2x)(4x) sq.ft
= (10x + 20x + 100) sq.ft
= (30x + 100) sq.ft
Finally, to find the total area of the patio AND the walkway, we add the area of the patio and the area of the walkway together.
Total area = Area of the patio + Area of the walkway
= 25 sq.ft + (30x + 100) sq.ft
= 30x + 125 sq.ft
Therefore, the correct answer is C. (x^2 + 25x + 125) sq.ft.