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User Anjelika
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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.

metaAI

User Sukhjeevan
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