Maths Polynomial Question

A piece of wire 2000cm long is used to make the edges of a cuboid (rectangular prism) with dimensions 2x, 3x and w.

a) Find w in terms of x.
b) Find the volume, V^3 in terms of x.
c) State the possible values of x.
d) Find the volume if x=50

Please Help. :)

Well, you have 4 edges of length 3x, 4 of length 2x, and 4 of length w.

So the total length of all the edges is

12x + 8x + 4w

= 20x + 4w = 2000

4w = 2000 - 20x

w = 500 - 5x

The volume, V = 6x^2(500 - 5x), or 3000x^2 - 30x^3

X can be any positive real number < 100, otherwise w <= 0

Plugging in 50 in the volume formula gives V = 3 750 000

a)In a cuboid,there are four edges of each dimension.A cuboid has three dimensions...So it's Perimeter = 4(2x) + 4(3x) + 4(w) = 2000,,,,8x + 12x + 4w = 2000,,,,,20x + 4w = 2000,,,,4w = 2000 - 20x,,,,w = 500 - 5x............................b) V = 2x * 3x * w,,,,,w=500-5x...V = 2x * 3x (500-5x),,,,V = 2x (1500x - 15x^2),,,, V = 3000x^2 - 30x^3,,,,V = 30x^2 (100 - x)cm^3..................................… 2(2x*3x) + 2(2x*w) + 2(3x*w) ,,,,,A = 2(6x^2) + 2(2x(500-5x)) + 2(3x(500-5x)) ,,,,,,A=12x^2 + 2000x - 20x^2 + 3000x - 30x^2,,,,,A= 12x^2 -50x^2 + 5000x ,,,, A= -38x^2 + 5000x ,,,,dA/dx = 2(-38)x + 5000 = 0 ,,,, -76x = -5000 ,,,,x = 1250/19 ....When you try dV/dx ,,x = 0 or 200...x = 0 (NA) because a dimension cannot be zero...x=200 is giving a value of w which is negative...i.e w=500-5(200) ,,,w = -500 (NA) which is impossible as a dimension cannot be negative...Therefore,x = 1250/19cm and w = 3250/19cm ...............................d)V = 30(50)^2 (100-50) ,,,,V=30*2500*50,,,,V=3750000cm^3 ,,,,V=3.75 * 10^6 cm^3.