SOLUTION: 3. A rectangular garden with an area of 96m^2 is 4m longer than it is wide. Find its dimensions. (Label the diagram. Solve using a quadratic eqaution!) Thank you very much!!!!

Question 200795: 3. A rectangular garden with an area of 96m^2 is 4m longer than it is wide. Find its dimensions. (Label the diagram. Solve using a quadratic eqaution!)
Thank you very much!!!!
Found 2 solutions by jim_thompson5910, rfer:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let L=length of garden and W=width of garden

Since the garden is "4m longer than it is wide", this tells us that

Now remember, the area of any rectangle is

Start with the area of a rectangle formula

Plug in (the given area) and

Rearrange the terms.

Distribute

Divide

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "W":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

However, you can't have a negative width. So the only solution is

So the width of the garden is 8 m.

Now add 4 m to 8m to get 4+8=12 m. So the length is 12 m

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Answer:

So the length and width of the garden are 12 meters and 8 meters.
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
w(4=4)=96
w^2+4w-96=0
b^2-4ac the discriminent
4^2-4(1)(-96)=0
16+384=400
x=(-4+ or- sq root of 400)/2(1)=8
x=8
w=8m
l=w+4=12m
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