If a rectangular lot measures 120 ft. x 80 ft., and 10 foot set backs are required from each lot line, how much area is left? If a kennel for 50 dogs requires 12,500 square feet, how many dogs can be accommodated in the small rectangle?
1)
L = 120 - 20 = 100
w = 80 - 20 = 60
A = Lw
A = 100 * 60
A = 6000 sq ft
2)
12,500/50 = 250 sq ft/dog
6000/250 = 24 dogs
To calculate the area left in the rectangular lot after considering the set backs, we need to subtract the set back areas from the total area of the lot.
1. Calculate the set back area for each side: Set back area = set back distance × lot width/length.
- Set back area for each long side = 10 ft × 120 ft = 1200 square ft.
- Set back area for each short side = 10 ft × 80 ft = 800 square ft.
2. Calculate the total set back area: Total set back area = set back area per side × number of sides.
- Total set back area = (1200 square ft × 2) + (800 square ft × 2) = 4000 square ft.
3. Calculate the area left: Area left = Total area of the lot - Total set back area.
- Total area of the lot = length × width = 120 ft × 80 ft = 9600 square ft.
- Area left = 9600 square ft - 4000 square ft = 5600 square ft.
Therefore, the area left in the rectangular lot after considering the set backs is 5600 square ft.
To determine how many dogs can be accommodated in the small rectangle given the kennel area requirement:
4. Determine the number of dogs per square foot: Dogs per square foot = Total number of dogs / Kennel area requirement.
- Kennel area requirement = 12,500 square ft.
- Dogs per square foot = 50 dogs / 12,500 square ft.
5. Calculate the area of the small rectangle:
- Small rectangle area = Area left (from Step 3).
6. Calculate the number of dogs that can be accommodated in the small rectangle:
- Number of dogs = Dogs per square foot × Small rectangle area.
Substituting the given values:
- Dogs per square foot = 50 dogs / 12,500 square ft ≈ 0.004 dogs/square ft.
- Number of dogs = 0.004 dogs/square ft × 5600 square ft ≈ 22.4 dogs.
Therefore, approximately 22 dogs can be accommodated in the small rectangle.
To find the area left after the setbacks, we need to subtract the setback area from the total area of the lot.
1. Calculate the setback area on each side:
- Setback on the shorter side: 10 ft x 2 = 20 ft
- Setback on the longer side: 10 ft x 2 = 20 ft
2. Subtract the setback area from the total area:
Total area = 120 ft x 80 ft = 9600 sq ft
Setback area = (20 ft + 20 ft) x (120 ft + 80 ft) = 40 ft x 200 ft = 8000 sq ft
Area left = Total area - Setback area = 9600 sq ft - 8000 sq ft = 1600 sq ft
Therefore, there is 1600 square feet of area left after the setbacks.
To determine how many dogs can be accommodated in the small rectangle of 1600 sq ft:
1. Calculate the area required per dog:
Area required per dog = Kennel area / Number of dogs
Area required per dog = 12,500 sq ft / 50 dogs
2. Divide the small rectangle area by the area required per dog:
Number of dogs accommodated = Area left / Area required per dog
Number of dogs accommodated = 1600 sq ft / (12,500 sq ft / 50 dogs)
Simplifying the equation:
Number of dogs accommodated = 1600 sq ft * (50 dogs / 12,500 sq ft)
Number of dogs accommodated = 64 dogs (rounded down to the nearest whole number)
Therefore, the small rectangle can accommodate approximately 64 dogs.