Asked by Anonymous
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
Answered by
Reiny
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
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