A child’s sandpit is rectangular with dimensions 2m x 1.5m. The sandpit is surrounded by a grassed area of uniform width covering an area of 24.5m^2
Calculate the uniform width of the grassed area
length of grass = 2 + 2 x
width of grass = 1.5 + 2 x
area of grass = (2x+2)(2x+1.5) - (2) (1.5) = 4 x^2 + 7 x + 3 - 3 = 4x^2+7x
4 x^2 + 7 x - 24.5 = 0 (I use https://www.mathsisfun.com/quadratic-equation-solver.html )
x =-3.5 or + 1.75
do not use negative width so 1.75
To calculate the uniform width of the grassed area, we need to subtract the area of the sandpit from the total area.
1. Find the area of the sandpit:
Area = Length × Width
Area = 2m × 1.5m
Area = 3m²
2. Calculate the total area (including the sandpit and the grassed area):
Total Area = Sandpit Area + Grassed Area
Total Area = 3m² + 24.5m²
Total Area = 27.5m²
3. The uniform width of the grassed area is the same on all sides. So, we need to find the square root of the total area to determine the width of the grassed area.
Uniform Width = √Total Area
Uniform Width = √27.5m²
Uniform Width ≈ 5.24m
Therefore, the uniform width of the grassed area is approximately 5.24 meters.
To calculate the width of the grassed area, we need to find the difference between the outer dimensions of the grassed area and the sandpit.
Let's start by calculating the area of the sandpit.
Area of the sandpit = length × width
= 2m × 1.5m
= 3m^2
Now, we can subtract the area of the sandpit from the total area to find the area of the grassed area.
Area of the grassed area = total area - area of the sandpit
= 24.5m^2 - 3m^2
= 21.5m^2
To find the width of the grassed area, we can divide the area of the grassed area by the total length of the sandpit.
Width of the grassed area = area of the grassed area ÷ length of the sandpit
= 21.5m^2 ÷ 2m
= 10.75m
Therefore, the uniform width of the grassed area around the sandpit is 10.75 meters.