The Roice family have a rectangular swimming pool. It measures 16' x 32'. This summer they are installing a sidewalk around the pool. The width of the sidewalk is yet to be determined,
1) Using the x as the width of the sidewalk, write a Polynomial to represent the perimeter of the sidewalk.
2) What is the area of the pool?
a) Using the x as the width of the sidewalk, write a polynomial to represent the area of the sidewalk and the pool together.
b) using the x as the width of the sidewalk, write a polynomial to represent the area of the sidewalk.
1) The perimeter of the sidewalk can be represented by the polynomial: P = 2(16 + x) + 2(32 + x)
2) The area of the pool is given by the product of its length and width. So, the area of the pool is: A = 16 * 32
a) The area of the sidewalk and the pool together can be represented by the polynomial: A_total = A + (16 + 2x)(32 + 2x)
b) The area of the sidewalk can be represented by the polynomial: A_sidewalk = (16 + 2x)(32 + 2x) - A
To determine the perimeter of the sidewalk, we need to add the dimensions of the pool and the sidewalk.
1) To represent the perimeter of the sidewalk, we sum the dimensions of the pool and twice the width of the sidewalk, since there are two lengths and two widths in a rectangle:
Perimeter = 2(Length + Width) + 2(Sidewalk Width)
Since the pool measures 16' x 32', the polynomial representing the perimeter of the sidewalk is:
Perimeter = 2(16 + x) + 2(32 + x) = 64 + 4x
2) The area of the pool can be determined by multiplying the length by the width:
Area of the Pool = Length x Width = 16' x 32' = 512 sq.ft.
a) To represent the area of the pool and the sidewalk together, we need to add the area of the pool to the area of the sidewalk:
Area of Pool + Area of Sidewalk = (16 + 2x)(32 + 2x)
b) To represent the area of the sidewalk only, we subtract the area of the pool from the total area of the pool and the sidewalk:
Area of Sidewalk = (16 + 2x)(32 + 2x) - 512 sq.ft.