Mathematics, 25.12.2020 21:20 SKYBLUE1015

A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

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Answer from: allyssaharrisooy50au

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 = ( $\frac{36}{y}$ + 2 )( y + 2 )

Now, Differentiating above equation and equating with 0 :

$3 -\frac{108}{y^{2} } = 0$

$\frac{3y^{2} - 108 }{y^{2} } = 0$

$3y^{2} - 108 = 0 \\3y^{2} = 108\\y^{2} = \frac{108}{3} \\y^{2} = 36\\y = 6$

then; xy = 36

6x = 36

x = $\frac{36}{6}$

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.

Answer from: kdenormandie3122

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 :

$3 - \dfrac{108}{y^2}=0\\\\y = \pm 6$

Now, we know dimension cannot be negative.

So, y = 6 and x = 6 .

Therefore, length and breadth are 6 and 6 inch respectively.

Answer from: Quest

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Answer from: Quest

The answer is budget i believe. hope this but it’s self explanatory.

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A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Fin...