Respuesta :
Given :
A rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
To Find :
The dimensions of the page such that the least amount of paper is used.
Solution :
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy ....1)
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, area of paper is :
A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( 36/y + 2 )( y + 2 )
Now, differentiating above equation and equating with 0 :
[tex]3 - \dfrac{108}{y^2}=0\\\\y = \pm 6[/tex]
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
The length are breadth is x = 6 and y = 6 inch respectively.
Given;
Each rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
We have to find ;
The dimensions of the page such that the least amount of paper is used.
Therefore,
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, Area of paper is : A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( [tex]\frac{36}{y}[/tex] + 2 )( y + 2 )
Now, Differentiating above equation and equating with 0 :
[tex]3 -\frac{108}{y^{2} } = 0[/tex]
[tex]\frac{3y^{2} - 108 }{y^{2} } = 0[/tex]
[tex]3y^{2} - 108 = 0 \\3y^{2} = 108\\y^{2} = \frac{108}{3} \\y^{2} = 36\\y = 6[/tex]
then; xy = 36
6x = 36
x =[tex]\frac{36}{6}[/tex]
x = 6inches
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
For more information about the Area of dimension click the link given below.
https://brainly.in/question/12894735
