cant have a negative height or width
Answer:
4 cm, 21.5 cm, and 31.5 cm
Explanation:
Let's work through the problem step by step!
We are given a cuboid with a volume of 924 cm³ and dimensions 4 cm, (x + 1) cm, and (x + 11) cm. We can start by using the formula for the volume of a cuboid, which is:
Volume = Length × Width × Height
In this case, the length is 4 cm, the width is (x + 1) cm, and the height is (x + 11) cm. Plugging these values into the formula, we get:
924 = 4(x + 1)(x + 11)
Now, we can expand and simplify the equation:
924 = 4x^2 + 44x + 44
Moving all the terms to one side, we get:
4x^2 + 44x - 924 = 0
Factorizing the left-hand side, we get:
(2x + 22)(2x - 41) = 0
This tells us that either (2x + 22) = 0 or (2x - 41) = 0.
Solving for the first factor, we get:
2x + 22 = 0 --> 2x = -22 --> x = -22/2 = -11
And solving for the second factor, we get:
2x - 41 = 0 --> 2x = 41 --> x = 41/2 = 20.5
Note that x cannot be -11, as it would make the width and height negative. Therefore, the only valid solution is x = 20.5.
So, the dimensions of the cuboid are:
4 cm, (20.5 + 1) cm, and (20.5 + 11) cm
Which simplifies to:
4 cm, 21.5 cm, and 31.5 cm
Therefore, the dimensions of the cuboid are 4 cm × 21.5 cm × 31.5 cm.
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