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.

Answer:15x^2 - 12x^3Step-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 = 204x + 12x + 4h = 2016x + 4h = 204h = 20 - 16xh = 5 - 4xNow 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^3Question 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