# Math

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The area of a rectangular photograph is 59 square inches.It is to be mounted on a rectangular card with a boarder of 1 inch at each side and 2 inches at the top and bottom.Express the total area of the photograph and the boarder,A, as a function of the width of the photograph,x.what width produces the maximum area

• Math -

let p = area of photo = 59
let x be the width. So, the height is 59/x

m = (x+2)(59/x + 4)
m = 59 + 118/x + 4x + 8

to find max mounted area, set m' = 0

m' = -118/x² + 4 = (4x² - 118)/x^2

So, m' = 0 when 4x²-118 = 0
x² - 29.5 = 0
x = 5.43"

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