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The volume of a box is 5x^3 + 20x^2 + 15x cm^3. If the height of the box is 5x cm, find the width and length of the box.

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Answer:

The product of the Width and Length is x^2 + 4x + 3 cm^2.

Explanation:

The volume of a box = 5x^3 + 20x^2 + 15x cm^3.

Volume of a Box = W*L*H [Width(W), Length(L), and Height(H)]

W*L*(5x) = 5x^3 + 20x^2 + 15x cm^3

W*L = (5x^3 + 20x^2 + 15x cm^3)/5x cm

W*L = x^2 + 4x + 3 cm^2

We know the area of the base of the box (W*L). It is x^2 + 4x + 3 cm^2.

To find the actual width and length, we need to know one of the variables, L or W. Without that, all we can say is that their product (W*L) is x^2 + 4x + 3 cm^2.

User Didier Ghys
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