Respuesta :
dimensions of the poster with margin are L = 12 in and h = 24 in
What is the area of a rectangular poster?
The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.
We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.
Rectangle area equals length times width.
Solution
Let call length of printed area of the poster be " x " and height of printed area of the poster be " y ".
Area of the poster = length and height
200 = x*y
y = 200/x
We also know that dimensions of the poster with margin is:
L = x + 2 in and H = y + 4 in
Therefore area of the poster is:
A(p) = ( x + 2 ) * ( y + 4 )
And area as function of x is:
A(x) = ( x + 2 ) * ( 200/x + 4 )
A(x) = 200 + 4*x + 400 /x + 8
Taking derivatives on both sides of the equation we have:
A´(x) = 4 - 400/x²
By taking A´(x) = 0
4 - 400/x² = 0 ⇒ 4*x² - 400 = 0
x² = 400 / 4
x² = 100
x = 10 in
and y = 200/x ⇒ y = 20
The second derivative A´´(x) = 400/x4 which is > 0
there is a minimum for the function at the point x = 10
As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are
L = x + 2 = 10 + 2 = 12 in and
h = y + 4 = 20 + 4 = 24 in
to learn more about area of rectangle visit:
brainly.com/question/28700994
#SPJ4
