Define variables
Let width = w (metres)
Length = w + 12 (metres)
Write the area equation
Area = Length × Width
11,200 = (w + 12)(w)
Expand equation
11,200 = w² + 12w
Rearrange into standard quadratic form
w² + 12w - 11,200 = 0
Solve quadratic (quadratic formula)
w = [-12 ± square root(12² - 4(1)(-11,200))] ÷ 2(1)
w = [-12 ± square root(144 + 44,800)] ÷ 2
w = [-12 ± square root(44,944)] ÷ 2
w = [-12 ± 212] ÷ 2
Find positive solution
w = (200 ÷ 2) = 100
Find length
Length = w + 12 = 100 + 12 = 112
Answer:
Width = 100 m
Length = 112 m