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8)A piece of plywood for a billboard has an area of 1.92 m2. The margins at the top and bottom are 0.20m and at the sides are 0.15m. Determine the dimensions of the plywood for maximum usabale area.

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Maximize usable area: 1.52m x 1.62m using standard plywood dimensions closest to 1.065 aspect ratio, minimizing waste.

Here's how to determine the dimensions of the plywood for maximum usable area:

1. Calculate the usable area:

First, subtract the margin heights from the total height: usable height = 1.92 m - 0.20 m (top) - 0.20 m (bottom) = 1.52 m.

Similarly, subtract the margin widths from the total width: usable width = 1.92 m - 0.15 m (left) - 0.15 m (right) = 1.62 m.

Multiply the usable dimensions to find the maximum usable area: usable area = 1.52 m x 1.62 m = 2.4864 m².

2. Find the aspect ratio:

Divide the usable width by the usable height: aspect ratio = 1.62 m / 1.52 m = 1.065.

3. Determine plywood dimensions:

Choose a standard plywood sheet size close to the aspect ratio. For example, a 2.44 m x 1.22 m sheet has an aspect ratio of 2:1, which is slightly wider than 1.065.

4. Minimize wasted space:

Adjust the plywood orientation to minimize wasted space. For the 2.44 m x 1.22 m sheet, use the 2.44 m length as the height and the 1.22 m width as the usable area (discarding 0.1 m on each side). This gives you a usable area of 2.38 m², slightly less than the maximum but with minimal waste.

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