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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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...

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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

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