Let
H ------------> the height of the printed area
W -----------> the width of the printed area
Then
we know that
HW = 162-------> H=162/W-----------> equation 1
the area of the poster is given by
A = (H + 4)*(W + 2)-----------> equation 2
I substitute 1 in 2
A=([162/W] + 4)*(W + 2)-----> A=162+324/W+4W+8
By taking the derivative,
Let A1------> derivative of A
we have
A1 = −324/W² + 4
By setting A1 to 0, we have
W²=324/4-------> W²=81------------> W=9 in
H=162/W----> 162/9-----> H=18 in
the dimensions of the poster are
(H + 4)-------> 18+4-----> 22 in
(W + 2)------> 9+2------> 11 in
the answer is
the dimensions of the poster are 11 in x 22 in
