Tom has a backyard that is 100ft. by 60 ft. He plans to install a rectangulr swimming pool bordered by a concrete walkway of uniform width. He wants the area of the pool to take up 1/2 of the area od the entire backyard. Determine the width of the walkway
yard area = 100*60 = 6000
pool area = 3000
now, if the pool has width x, length y, and the walkway is w wide, we have
(x+2w)(y+2w) = 3000
Unfortunately, that's where we have to pause. You could have a tiny pool with a wide border, or a large pool with a skinny border.
Sure there's not something you're missing?
The only other thing it says is round your answer to 2 decimals.
13.2
To determine the width of the walkway, we need to calculate the area of the pool and the area of the entire backyard first. Then, we can find the width that makes the pool area equal to half of the total backyard area.
1. Calculate the area of the entire backyard:
Area = Length * Width
Backyard Area = 100 ft * 60 ft = 6000 square ft
2. Determine the area of the pool that should take up half of the backyard area:
Pool Area = 1/2 * Backyard Area = 1/2 * 6000 square ft = 3000 square ft
3. Let's assume the width of the walkway is "w" feet.
The length and width of the pool will be reduced by twice the width of the walkway since the walkway surrounds the pool on all sides.
Length of the pool = Length of the backyard - 2 * Width of the walkway
Width of the pool = Width of the backyard - 2 * Width of the walkway
Pool Area = Length of the pool * Width of the pool
3000 square ft = (100 ft - 2w) * (60 ft - 2w)
4. Expand the equation and solve for the width of the walkway:
3000 square ft = (100 ft - 2w) * (60 ft - 2w)
3000 square ft = 6000 ft^2 - 200 ft * w - 120 ft * w + 4w^2
4w^2 - 320w + 3000 = 0
We can now solve this quadratic equation to find the values of "w" that satisfy the equation.