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!!!!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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!!!!      Log On


   

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) About Me  (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 L=W%2B4

Now remember, the area of any rectangle is A=LW


A=LW Start with the area of a rectangle formula


96=%28W%2B4%29W Plug in A=96 (the given area) and L=W%2B4


96=W%28W%2B4%29 Rearrange the terms.


96=W%5E2%2B4W Distribute


0=W%5E2%2B4W-96 Divide


Notice that the quadratic W%5E2%2B4W-96 is in the form of AW%5E2%2BBW%2BC where A=1, B=4, and C=-96


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


W+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


W+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%28-96%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=-96


W+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-96%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


W+=+%28-4+%2B-+sqrt%28+16--384+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-96%29 to get -384


W+=+%28-4+%2B-+sqrt%28+16%2B384+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--384%29 as sqrt%2816%2B384%29


W+=+%28-4+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 Add 16 to 384 to get 400


W+=+%28-4+%2B-+sqrt%28+400+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


W+=+%28-4+%2B-+20%29%2F%282%29 Take the square root of 400 to get 20.


W+=+%28-4+%2B+20%29%2F%282%29 or W+=+%28-4+-+20%29%2F%282%29 Break up the expression.


W+=+%2816%29%2F%282%29 or W+=++%28-24%29%2F%282%29 Combine like terms.


W+=+8 or W+=+-12 Simplify.


So the possible solutions are W+=+8 or W+=+-12


However, you can't have a negative width. So the only solution is W=8

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) About Me  (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