Question

a rectangular poster is to contain 242 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?

Answer 1

To find the dimensions of the poster that will use the least amount of paper, we need to consider the area of the printed portion and the margins. Substitute the values into the formula and find the value of x that minimizes the total area of the poster.

Step-by-step explanation:

To find the dimensions of the poster that will use the least amount of paper, we need to consider the area of the printed portion and the margins.

The total area of the poster, including the margins, is given by the formula:

Total Area = (Length + 2) * (Width + 2)

Let's assume the width of the printed portion is x inches. So, the length of the printed portion is (242/x) inches.

Now, we can substitute these values into the formula and find the value of x that minimizes the total area of the poster.

Answer 2

To minimize the use of paper, the dimensions of the poster should be 3 inches by 2 inches.

Step-by-step explanation:

To find the dimensions of the poster that would use the least amount of paper, we need to minimize the total area. The total area of the poster can be found by calculating the product of the dimensions of the printed area.

The printed area is the length of the poster minus the margins on the left and right, multiplied by the width of the poster minus the margins at the top and bottom. Let's assume the length of the printed area is x inches and the width is y inches.

Given that the margins on the top and bottom are 2 inches and the margins on the left and right are 1 inch, the dimensions of the poster can be expressed as:

x = y - 2

y = x - 1

Substituting the second equation into the first equation, we get x = (x - 1) - 2, which simplifies to x = x - 3. Solving for x, we find x = 3. Substituting this value back into the second equation, we get y = 3 - 1, which simplifies to y = 2.

Therefore, the dimensions of the poster that would use the least amount of paper are 3 inches by 2 inches.