A square patio is surrounded by a brick walkway. What is the total area of the patio AND the walkway?
5ft
a. (x^2 + 15x + 50) sq.ft
b. (x^2 + 10x + 25) sq.ft
c. (x^2 + 20x + 100) sq.ft
d. (x^2 + 25x + 125) sq.ft
To find the 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 can be found by squaring the length of one side of the square, which is 5ft. So the area of the patio is 5^2 = 25 sq.ft.
The walkway surrounds the patio, so it is an extra layer around the patio. If the width of the walkway is x ft, then the outer side of the walkway will be 5+x+5 = 10+x ft long.
Therefore, the area of the walkway is (10+x) * (10+x) = (10+x)^2 sq.ft.
To find the total area, we add the area of the patio to the area of the walkway:
Total area = Area of patio + Area of walkway
= 25 sq.ft + (10+x)^2 sq.ft
Simplifying this expression, we have:
Total area = 25 + 100 + 20x + x^2 sq.ft
= 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 d. (x^2 + 25x + 125) sq.ft