Answer:
Width = 139.445 ft and Length = 1721.11 ft or
Width = 860.555 ft and Length = 278.89 ft
Step-by-step explanation:
If the school has a rectangular shape, we have that its perimeter and area are:
Perimeter = 2*Length + 2*Width
Area = Length * Width
If we just want to cover 3 sides of the school, we can affirm that:
2000 = Length + 2*Width (eq1)
And the area is 240,000 ft2, so:
240000 = Length * Width (eq2)
From (eq1), we have that:
Length = 2000 - 2*Width
Using this value in (eq2), we have:
240000 = (2000 - 2*Width) * Width
240000 = 2000*Width - 2*Width^2
Width^2 - 1000*Width + 120000 = 0
Using Bhaskara's formula, we have:
Delta = 1000^2 - 120000*4 = 520000
sqrt(Delta) = 721.11
Width1 = (1000 + 721.11)/2 = 860.555 ft
Width2 = (1000 - 721.11)/2 = 139.445 ft
If we use Width = 139.445 ft, we will find Length = 1721.11 ft
If we use Width = 860.555 ft, we will find Length = 278.89 ft
Both pairs of dimensions are valid answers, as they would use 2000 feet of gate and the area of the school would be 240,000 ft2
