A poster requires 144 cm^2 for the printed message and must have a 4 cm margin on each side. Determine the overall dimensions of the poster and determine the least amount of paper required.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The posters that are made should have 144 cm^2 of area for text. There has to be a margin of 4 cm on all the sides. It is assumed that the poster is made in the shape of a rectangle. Let one of the sides be of length x. The other side has a length `144/x` . The area of the margin is `2*4*(x + 8) + 2*4*(144/x)`

The total area of the paper required is `A = 144 + 2*4*(x + 8) + 2*4*(144/x)`

=> A = `144 + 8x + 64 + 1152/x`

A' = `8 - 1152/x^2`

`8 - 1152/x^2 = 0`

=> `x^2 = 144`

=> `x = 12`

The least amount of paper used to make the poster is 400 cm^2

etotheeyepi's profile pic

etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted on

If the poster were circular

Written area = 144 cm^2

radius or written area = (144/pi)^.5 = 6.77 cm

radius of poster = 6.77 +  4 = 10.77 cm

Area of poster = pi*(10.77)^2 = 364 cm^2

gultekin's profile pic

gultekin | Student, Undergraduate | eNotes Newbie

Posted on

i didnt get the area of the margin where did you get (x+8) from?

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