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