Answer :
The Poster Dimensions of rectangle will be:
W = 18 inches
Y = 36 inches
Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (square centimeters, square inches, square feet, etc.). The area of a rectangle is the number of unit squares that fit in the rectangle. Examples of rectangles are flat surfaces such as laptop monitors, chalkboards, and painting canvases. You can use the rectangle area formula to find the space occupied by these objects.
Now,
Let's say the printable area of a rectangular poster is 512 square inches
"x". " and "y" - the dimensions of the printed area of the poster
A(p) = printed area of the poster = x × y
512 = x × y ⇒ y = 512/x
Therefore, The total area of the poster is:
A( t) = ( y + 4 ) × ( x + 2 )
⇒ A(t) = yx +2y +4x + 8 and y = 512/x
Total Area of x or Total poster area as x function:
A(x) =( 512/x)*x + 2* (512/x) + 4*x + 8
A(x) = 512 + 1024/x + 4 *x + 8
⇒ A(x) = 520 + 1024/x + 4*x
Differentiating both sides of the equation gives:
A´(x) = - 1024/x² + 4
A´(x) = 0
⇒ - 1024 /x² = -4
⇒ 4*x² = 1024
⇒ x² = 1024/4
⇒ x² = 256
or, x = 16 inches
and y = 512/x
⇒ y = 512/16
⇒ y = 32 inches
So x is found, the y dimension of the print area, Than n is the dimension of the poster:
Therefore,
w = x + 2 ⇒ w = 16 + 2 w = 18 in
And,
Y = y + 4 ⇒ Y = 32 + 4 Y = 36 in
Learn more about Dimensions:
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