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goldfiish [28.3K]
3 years ago
11

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

e garden

Mathematics
1 answer:
inna [77]3 years ago
4 0

Answer:

Length = 18.099 ft

Width = 11.049 ft

Step-by-step 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=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

Solving first

y=\frac{2+\sqrt{4+400}{2}

y=\frac{2+\sqrt{404}{2}

y=\frac{2+20.099}{2}

y=\frac{22.099}{2}

y=11.049

Solving second one

y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

y=\frac{2-\sqrt{4+400}{2}

y=\frac{2-\sqrt{404}{2}

y=\frac{2-20.099}{2}

y=\frac{-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

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