Math Problem?

Question

Sports: The length of the field in field hockey is 20 yd less than twice the width of the field. The area of the field in field hockey is 6000 yd^2. Find the length and width of the field.

Answer 1

Let w = width

Then 2w - 20 = length

Area = L x W

w(2w - 20) = 6000
2w² - 20w - 6000 = 0

Divide thru by 2
w² - 10w - 3000 = 0

(x + 50)(x - 60) = 0

The negative solution (x = -50) is trivial.

x = 60 yds - width

2*60 - 20 = 100 yds - length

Answer 2

Area of Rectangle = Length x Width

Let L be length and W be the width of the hockey field:

A = L x W

6000 = L x W

Since L = 2W - 20
(ie The length of the field in field hockey is 20 yd less than twice the width of the field)

=> 6000 = (2W -20)W

6000 = 2W^2 - 20W
0 = 2W^2 -20W -6000
0=W^2 -10W - 3000

W = 60, -50

Since length cannot be negative, we will take the 60 yd answer for the width.

Substitute back to the Length equation:

L = 2W - 20 = 2(60) - 20 = 100 yd

Answer 3

I hope this is right:

make the width x. And the length is 2x-20 since its twice the width and minus 20

so: x * (2x-20) = 6000
2x^2 - 20x = 6000
2x^2 - 20x - 6000 = 0
Reduce
x^2 - 10 x - 3000 = 0

factor
(x-60) (x+50) = 0
x= 60, -50.
take out -50 since it there cannot be negative length

plug 60 into each x
width = 60
length = 2(60) - 20 = 100

Answer 4

We know the length, let's say "L" is 2 times the width minus 20. Or...

L=2*W-20
we also know the area is L*W, so the area "A" would be

A=W*(L)
A=W*(2*W-20)
A=2*W^2 - 20W

The area is 6000 so

6000=2W^2-20W

divide through by 2!

3000=W^2-10W

W^2 - 10W - 3000=0

Break it down into (W+50)(W-60)
clearly negatives dont work for distance so our only solution is W=60.

Check it...

Width = 60
Length is 100 (2*60 -20 =100)

And 60*100 = 6,000

~Sky

Answer 5

let x = width of the field
2x - 20 = length of the field

x(2x - 20) = 6000
2x^2 - 20x - 6000 = 0
x^2 - 10x - 3000 = 0
(x - 60)(x + 50) = 0

x + 50 = 0
x = -50
x - 60 = 0
x = 60
2x - 20
2(60) - 20
120 - 20
100
the width of the field is 60 yd
its length is 100 yd
^.^