A rectangle field with area of 300 square meters and a perimeter of 80 meters. What are the length and width of the field?

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changchengliang eNotes educator | Certified Educator

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Our task is to find out the length and width of the field.

Let the length of the field be L and the width of the field be W

 

Area of rectangle is given by  A=L*B .

Perimeter of rectangle is given by  P=2(L+B).

 

Using information given by the question we have the following 2 equations:

L*B = 300  ......(1)

2(L+B) = 80 ......(2)

Since we have two unknowns and two equations, we can solve the simultaneous...

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hala718 eNotes educator | Certified Educator

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bonniegknight | Student

Let L represent length, let W represent Width.

Perimeter is equal to 2L+2W for any rectangle, or P=2L+2W

Area is equal to L*W for any rectangle, or A=L*W

Here, the perimeter is 80 meters and the area is 300m^2.  How can we use this information to find out answers?  Let's think and figure it out.

L*W=300m^2

2L+2W=80m >>>>>>>> 2(L+W)=80>>>>>>> (L+W)=80/2 =40

L+W=40 then L=40-W  OR W=40-L  Choose one or the other to use in the equation for area.

A=L*W>>> 300m^2 = L*(40-L)

300m^2=40L-L^2 >>>>>>rewrite>>> L^2-40L+300=0 >>>now solve for L by factoring this equation to get (L-30)(L-10)=0 Therefore L=30 or L = 10.  It would make more sense that the length would be the longest dimension so we will say that L=30.  Then W would have to be 10.  The rectangle is 30m long and 10m wide.  Just to be sure, let's multiply L*W to see if we get 300m^2, which we know is the area of this rectangle.

Is 10*30 = 300?  Yes, it is.  Therefore 10m*30m=300m^2

Now lets check the Perimeter: 80 = 2L+2W OR 80 = 2*30 + 2*10  >>>> 60+20=80  Is that correct?  I think it is.  Now you have your solution.  The length of this rectangle is 30 meters and the width of it is 10 meters.  That wasn't too difficult, was it? 

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neela | Student

Perimeter of arectangle P = 2(l+w), where l = length and w = width of the rectangle.

Given the perimeter  of the rectangular field , P = 80 m. So the l = P/2 -w = 80/2 -w.

Therefore the area of the rectanglar field = l*w = (80/2 - w)w . But are is given to be 300 sq m.

So the required equation is :

(80/2-w)w = 300.

(40-w)w = 300.

40w - w^2 = 300.

40w - w^2 -300 = 0

Multiply by (-1) and write as below:

w^2 -40w +300 = 0.

w^2 -30w -10 w +300 = 0.

w(w-30) -10(w-30) = 0.

(w-30) (w-10) = 0.

Therefore w -30 = 0, Or w -10 = 0.

So w-30 = 0 gives w = 30, and w-10 = 0 gives w = 10.

Therefore w = 10 m  and  l = (80/2 -10) = 30 m

So  length = 30 meter and width = 10 m.

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