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A certain rectangular prism has a height of 4 m, a length of 6 m, and a width of 8 m. Give the dimensions of a second rectangular prism that will have the same surface area of the first one.

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Step-by-step explanation:

in its basic structure such a prism is like a cube (just rectangular and not squared) : 6 sides (rectangles).

2 rectangles top and bottom 6×8 = 48 m²

48 × 2 = 96 m²

2 rectangles front and back 6×4 = 24 m²

24 × 2 = 48 m²

2 rectangles left and right 8×4 = 32 m²

32 × 2 = 64 m²

the total surface area is

96 + 48 + 64 = 208 m²

it is hard to find other integer dimensions for the same surface area.

but as long as we are not restricted to integer numbers :

let's cut e.g. the height in half.

and we get

2 rectangles left and right 8×2 = 16 m²

16 × 2 = 32 m²

that "nails" already 2 dimensions (width and height).

we need to set now the third dimension (length) to create the same surface area :

length×8×2 + length×2×2 = 208 - 32 = 176

20×length = 176

length = 8.8 m

so, with

length = 8.8 m

width = 8 m

height = 2 m

we still get

2 rectangles top and bottom 8.8×8 = 70.4 m²

70.4 × 2 = 140.8 m²

2 rectangles front and back 8.8×2 = 17.6 m²

17.6 × 2 = 35.2 m²

2 rectangles left and right 8×2 = 16 m²

16 × 2 = 32 m²

as total surface area

140.8 + 35.2 + 32 = 208 m²
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