Question
A graphic designer is asked to create a movie poster with a 128 in^2 photo surrounded by a 4 in border at the top and bottoms and a 2 in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?
Answers
let the width of the photo be x in
then the length of the photo is 128/x in
width of poster = x+8
length of poster = 128/x + 8
Area = (x+8)(128/x + 8)
= 128 + 8x + 1024/x + 64
d(area) = 8 - 1024/x^2
= 0 for a min of area
8 = 1024/x
8x^2 = 1024
x^2 =128
x = √128 = 8√2
carry on
then the length of the photo is 128/x in
width of poster = x+8
length of poster = 128/x + 8
Area = (x+8)(128/x + 8)
= 128 + 8x + 1024/x + 64
d(area) = 8 - 1024/x^2
= 0 for a min of area
8 = 1024/x
8x^2 = 1024
x^2 =128
x = √128 = 8√2
carry on