SOLUTION: the area of a rectangular parcel of land is 720 sq. meters. the length of the land is 4 meters less than twice the width. a. write an equation than can be used to find the dimensi

Question 143174This question is from textbook
: the area of a rectangular parcel of land is 720 sq. meters. the length of the land is 4 meters less than twice the width.
a. write an equation than can be used to find the dimensions of the land.
(i think i have this- 720=(2w-4)w)
b.solve the equation in part a. to find the dimensions of the land
Note: i already have the answer(l=36,w=20), i just don't know how to solve the equation) This question is from textbook

Found 2 solutions by jim_thompson5910, rapaljer:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a) you have the correct equation

b)

Start with the given equation

Distribute

Distribute

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for w in each case

So our possible widths are
or

However, since a negative width doesn't make sense, this means that the width is

Now go back to the length equation

Plug in

Multiply

Subtract

So our answers are and

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Multiply out the parentheses. Since it's quadratic, you have to set it equal to zero:
720=(2w-4)w
720=2w^2 - 4w
0=2w^2 -4w -720

Factor completely, beginning with the common factor of 2:
0=2(w^2 -2w-360)

Factor the trinomial:
0=2(w+18)(w-20)

w=-18 or w=20

Reject the negative answer since a width cannot be negative.
So, w=20 meters
2w-4=2(20)-4=40-4=36 meters

Check:
Area = W*L
Area = 20*36=720 square meters

R^2
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