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7 April, 05:28

a rectangular block is such that the sides of its base are of the length x cm and 3x cm. The sum of all the lengths of all its edges is 20cm. Find the volume.

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  1. 7 April, 05:45
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    15x^2 - 12x^3

    Step-by-step explanation:

    A rectangular block has 3 parts that play into its volume. length, width and height. The question gives us length and width in the form of x and 3x, so height is what's missing.

    It gives us a bit more information saying the sum of its edges is 20. We also have to ask how many lengths, widths and heights are there. That may be a bit hard to understand, but is you are looking at a block I could ask how many edges are vertical, just going up and down. These would be the heights. There are 4 total, and this goes the same for length and width, so 4*length + 4*width and 4*height = 20.

    Taking that and plugging in x for length and 3x for width (or you could do it the other way around, it doesn't matter, you get:

    4*x + 4*3x + 4*height = 20

    4x + 12x + 4h = 20

    16x + 4h = 20

    4h = 20 - 16x

    h = 5 - 4x

    Now we have h in terms of x, which lets us easily find the volume just knowing x. To find the volume of a rectangular block you just multiply the length, width and height.

    x*3x * (5-4x)

    3x^2 (5-4x)

    15x^2 - 12x^3

    Question doesn't give a specific value for x at all so you should be done there. Any number you plug in for x should get you the right answer
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