Answer:
lenght 19 in
width 19 in
Explanation:
Let x and y be dimensions of print area, that is
x*y = 81 in² then y = 81/x
then total area of the poster is (including top, bottom and sides margins)
( x + 10 )*( y + 10 ) = A(t)
A(x) = ( x + 10 )*( 81/x + 10 ) solving
A(x) = 81 + 10x + 810/x + 100
Taking derivatives both sides of the equation
A´(x) = 10 - 810/x²
A´(x) = 0 10 - 810/x² = 0 (10x²-810)/x² = 0
10x² - 810 = 0
x² = 81
x = 9 in then y = 81/x y = 81/9 y = 9 in
Then remember, these are values for the print area, now we have to add 10 inches according to margins
The dimensions of the poster will be
lenght 19 in
width 19 in