Question

The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of the garden

Answer 1

Length = 18.099 ft

Width = 11.049 ft

Explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4 -----------(A)

Also the area is given as 200 sqft

Hence

xy=200

Hence from A we get

y(2y-4)=200

taking 2 as GCF out

2y(y-2)=200

Dividing both sides by 2 we get

`y(y-2)=100`

`y^2-2y=100`

subtracting 100 from both sides

`y^2-2y-100=0`

Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

`ax^2+bx+c=0`

Here in our case

a=1

b=-1

c=-100

Putting those values in the formula and solving them for y

`y=(-(-2)+√((-2)^2-4 * (-1) * 100))/(2 \time 1)`

`y=(-(-2)-√((-2)^2-4 * (-1) * 100))/(2 \time 1)`

Solving first

`y=(2+20.099)/(2)`

`y=(22.099)/(2)`

`y=11.049`

Solving second one

`y=(-(-2)-√((-2)^2-4 * (-1) * 100))/(2 \time 1)`

`y=(2-20.099)/(2)`

`y=(-18.99)/(2)`

`y=-9.045`

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

Width = 11.049 ft