Let's plug in each coordinate and see what we get:
(2, 0, 0) -> 2A + 0 + 0 = D -> 2A = D -> A = D/2
(0, 6, 0) -> 0 + 6B + 0 = D -> 6B = D -> B = D/6
(0, 0, 5) -> 0 + 0 + 5C = D -> 5C = D -> C = D/5
plugging this back into the equation: (D/2)x + (D/6)y + (D/5)z = D [then divide through by D] (1/2)x + (1/6)y + (1/5)z = 1 and since we have to have integer coefficients, multiply through by 30
so we get 15x + 5y + 6z = 30
Second question
<span>Take a look at the bottom-left point in the picture. If you move three points in the y-direction, you'll reach to the point A. If you instead move up 4 points (or in the z-direction), you reach D. And finally, if you walk back to point F from point E, you'll have moved back 4 points in the x direction. </span>
<span>This gives us our measurements, or dimensions: 3 x 4 x 4. If this were a rectangular prism, the dimensions would just be each of them multiplied. But since it's triangular, you need to divide it by two. That gives you a total volume of (3x4x4)/2 = 24.</span>
