The length of a soccer pitch is 20 m less than twice its width. the area of the pitch is 6000m^2. find its dimensions.

X=width of a coccer pitch

2x-20=length of a soccer pitch

Area (rectangule) = length x width

We suggest this equation:

x (2x-20) = 6000

2x²-20x=6000

2x²-20x-6000=0

x²-10x-3000=0

We solve this quadratic equation:

x=[10⁺₋√ (100-4*1*-3000) ]/2=[10⁺₋√ (100+12000) ]/2=

= (10⁺₋110) / 2

we have two solutions:

x₁ = (10-110) / 2=-50, invalid solution.

x₂ = (10+110) / 2=60

x=60

2x-20=2 (60) - 20=120-20=100

Solution: the length is 100 m, and the width is 60 m.

To check:

Area=100 m*60 m=6000 m²

The twice of width is = 2 (60 m) = 120 m,

20 m less than twice its width is: 120 m-20 m=100 m=the length.