Jack wants to install a swimming pool that is 12m long and 8m wide. He wants to install a rubberized safety border of uniform width around the pool. The width of the safety border is represented by x and the area of the safety border is 44 m^2.
a) Write an expression in terms of x for the length and width dimensions of the outside safety border.
b) What is the total area of the pool and border?
c) Write a quadratic equation that could be used to calculate the width of the safety border.
d) How wide is the safety border around the pool?
(a) 12+2x and 8+2x
(b) (12+2x)(8+2x)
(c) (12+2x)(8+2x)-12*8
(d) ...
a) To find the dimensions of the outside safety border, we need to add the width of the border to both the length and the width of the pool.
The length of the outside safety border would be the sum of the pool's length and twice the width of the border (since there is a border on both sides of the pool):
Length of outside safety border = 12m + 2x
Similarly, the width of the outside safety border would be the sum of the pool's width and twice the width of the border:
Width of outside safety border = 8m + 2x
b) The total area of the pool and the border can be calculated by multiplying the length of the outside safety border by the width of the outside safety border:
Total area = (12m + 2x) * (8m + 2x)
c) To write a quadratic equation that could be used to calculate the width of the safety border, we need to use the area information given. The area of the safety border is 44 m^2. This can be expressed as the difference between the total area and the area of the pool:
(12m + 2x) * (8m + 2x) - 12m * 8m = 44
Simplifying this expression, we have:
(12m + 2x) * (8m + 2x) - 96m^2 = 44
d) To find the width of the safety border, we need to solve the quadratic equation. However, without a specific value for x, it is not possible to determine the exact width. The quadratic equation can be used to find the possible values for x, and then those values can be checked to see if they make sense in the given context.