The surface area of the cuboid below is 284 cm².
Calculate X.
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The surface area of the cuboid below is 284 cm².
Calculate X.
To solve for , we begin with the formula for the surface area of a cuboid:
, where , , and .
Substitute the given surface area into the formula:
Simplify the equation by first expanding each term inside the parentheses:
Combine like terms:
Divide both sides by 2 to isolate the linear expression:
Subtract 54 from both sides to solve for :
Finally, divide by 22 to find :
Therefore, the solution to the problem is .
4
Identify the correct 2D pattern of the given cuboid:
A cuboid has 6 faces: 2 faces of area ab, 2 faces of area bc, and 2 faces of area ca. The formula accounts for all pairs of opposite faces.
Since we're dealing with dimensions of a real object, all measurements must be positive. If x-3 < 0, the problem has no realistic solution. In this case, x = 4 gives us x-3 = 1, which is positive!
Use the distributive property: (x-3)(12) = x(12) + (-3)(12) = 12x - 36. Don't forget the negative sign when multiplying -3 by 12!
While substitution is the most reliable check, you can also verify that your x-value makes physical sense. Since x-3 = 1 when x = 4, all dimensions (10, 1, 12) are positive, which is required for a real cuboid.
Decimal answers are perfectly valid! Just make sure to double-check your arithmetic and substitute back to verify. However, in this problem, the clean numbers suggest the answer should be a whole number.
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