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.

Answers: 2

Show answers

Answers

answered: 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.

answered: 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.

answered: Guest

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

answered: Guest

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:10, michaelwthms

To describe a sequence of transformations that maps triangle abc onto triangle a"b"c", a student starts with a reflection over the x-axis. how should the student complete the sequence of transformations to map triangle abc onto triangle a"b"c"? plz

Answers: 1

continue

Mathematics, 21.06.2019 18:00, ineedhelp2285

How to do this , and can some one explain

Answers: 1

continue

Mathematics, 21.06.2019 19:30, gabby77778

[15 points]find the least common multiple of the expressions: 1. 3x^2, 6x - 18 2. 5x, 5x(x +2) 3. x^2 - 9, x + 3 4. x^2 - 3x - 10, x + 2 explain if possible

Answers: 3

continue

Mathematics, 21.06.2019 23:00, leverso

You buy a veido game for $60 and the sales tax is 8% what is the total cost for the game including the sales tax

Answers: 1

continue

Do you know the correct answer?

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