The perim. of a rect. rose garden is 140m &area is 1200m^2. Find the length and the width.?

♦ p= x+y+x+y =2x+2y, hence y=(p-2x)/2;


A=x*y =x*(p/2-x); now numbers →


♣ 1200 = x*(140/2-x); → x^2 –70x +1200 =0,


hence x,y =35 ±√(35^2 –1200) =30, 40;

The perim. of a rect. rose garden is 140m %26amp;area is 1200m^2. Find the length and the width.?
Hello





So the dimensions of the rectangle is x, x, y, y.





So we have 2x+2y = 140 and xy=1200.





Lets substitute x = 1200/y into the first equation to get:


2(1200/y) + 2y = 140.





2400/y + 2y = 140.


Mult both sides by y to get 2400 + 2y^2 = 140 y





Rearrange to get: 2y^2 - 140y + 2400 = 2(y^2-70y+1200).





This is 2(y-30)(y-40).





So the solution is 30 and 40.





Hope this helps
Reply:2l+2w=140


l x w =1200


2w=140-2l, w=70-l


substitute this into l x w =1200, to get


l(70-l)=1200


70l -l^2=1200


-l^2+70l-1200=0


l^2-70l+1200=0


(l -30)(l-40)=0


l=30 or l=40


if l=30,w=40 and if l=40 w=30


Since length is usually the longer dimension,


the answer is l=40, w=30
Reply:Let the length and width of the garden be x and y meters respectively


Therefore,


2(x+y)=140 or x+y=70 and


xy=1200


We know that


(x-y)^2=(x+y)^2-4xy


=(70)^2=4*1200


=4900-4800=100


or,x-y=10 [square-rooting both sides]


Now, we have two linear equations,


x+y=70,and


x-y=10


solving these,we get


x=40 and y=30


Therefore,the length of the garden is 40 m and the width is 30 m
Reply:LxB=1200 sq m--------------(1)


%26amp;2(L+B)=140 m


or L+B=140/2=70 m--------(2)


or L=70-B----------------------(3)





From (1) %26amp;(3),we have


(70-B)xB=1200


or B^2-70B+1200=0


or B^2-30B-40B+1200=0


or B(B-30)-40(B-30)=0


or( B-30)(B-40)=0


B=30 or B=40


Since Breadth is always smaller,so let us say


B=30-----------------(4)


from (1) %26amp; (4),we have


L x B= 1200


so L =1200/B=1200/30=40


so L=40 m %26amp; B=30 m ans
Reply:Let L = length


Let W = width





The perimeter of the garden will be


P = 2L + 2W





The area will be


A = L*W





We have 2 unknowns (length and width) and 2 equations





2L + 2W = 140


L * W = 1200





Divide the bottom equation by L to get


(L*W)/L = 1200/L


W = 1200/L





Plug this into the other equation





2L + 2W = 140 divide both sides of the equation by 2 to get


L + W = 70


L + 1200/L = 70


Multiply both sides by L


L^2 + 1200 = 70L


L^2 - 70L + 1200 = 0


(L - 30)(L - 40) = 0





L=30 L = 40





2L + 2W = 140


2(40) + 2W = 140


80 + 2W = 140


2W = 60


W = 30





So the width is 30m and the length is 40m