A rectanglular swimming pool has a length of 25 feet and a width of 12 feet. You want to a gravel walkway that is 4 feet wide all the way around the pool. What is the area of the gravel walkway
You want to put a fence in the shape of a rectangle around your new house. The fence you want to purchase is $7.00 per foot and you have a budjet of $2,100. What is the maximum area that you are able to fence with your budget
total area = (25+8)(12+8)
water surface area = 25*12 = 300ft^2
subtract
fence length = 300 feet
max is a square
300 = 4s
s= 300/4 = 75
area = s^2 = 5625
Now do you know way the biggest rectangle area for 300 foot fence is a square?
fence = 2 L + 2 w = 300
so
L = 150 - w
A = L W
A = (150-w)w = 150 w - w^2
so
w^2 -150 w = - A
w^2 - 150 w + 75^2 = -A + 5625
vertex at
w = 75
area = 5625
To find the area of the gravel walkway, we need to subtract the area of the pool from the area of the entire rectangle which includes the pool and the walkway.
First, let's calculate the area of the entire rectangle, including the walkway. The length of the rectangle is 25 feet, and the width is 12 feet. So, the area of the entire rectangle is:
Area of rectangle = Length × Width
= 25 feet × 12 feet
= 300 square feet
Next, we need to subtract the area of the pool itself, which is 25 feet long and 12 feet wide, from the area of the rectangle. The area of the pool is:
Area of pool = Length × Width
= 25 feet × 12 feet
= 300 square feet
Finally, we subtract the area of the pool from the area of the entire rectangle to find the area of the gravel walkway:
Area of gravel walkway = Area of rectangle - Area of pool
= 300 square feet - 300 square feet
= 0 square feet
Since the area of the gravel walkway is 0 square feet, it means that there is no walkway around the pool.