The surface area of a rectangular solid is 192 cm 2 . If the height of the solid is 4 units and the length of the solid is 12 units, what is the width of the solid?

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The surface area of a solid is the sum of the areas of each side of the solid. A rectangular solid has 6 rectangular faces. If w is the width of the solid, then two faces measure 4 units by 12 units, two faces measure 4 units by w units, and two faces measure 12 units by w units. Therefore, the surface area of the solid is equal to 2(4 × 12) + 2(4 × w) + 2(12 × w) = 96 + 8w + 24w = 96 + 32w. Since the surface area of the solid is 192 cm 2 , 96 + 32w = 192, 32w = 96, w = 3. The width of the solid is 3 units.

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