a question about prisms?

Question

the height, width, and length of a rectangular prism are in the ratio 1:2:4. if the surface area of the prism is 17,500cm^2, write an equation to model the problem and find the dimensions (height, width, and length) of the prism.

if you know the answer, plz tell me how you got it..like the formulas and stuff. thx!

Answer 1

If the ratio is 1:2:4, then the dimensions are x, 2x, and 4x, for some x. In any rectangular parallelpiped - length L, width w, and height h - the surface area is S = 2(Lw + Lh + wh). We already know the surface area to be 17,500, so use that for S, and use x, 2x, and 4x for the length, width and height, in any order, and solve for x.

Answer 2

A = 2(HW +LW+LH) = 17,500 cm^2
W = 2H
L = 4H
2(2H*H + 2H*4H + 4H*H) = 17,500 cm^2
H^2(2 + 8 + 4) = 8,750cm^2
14H^2 = 8,750cm^2
H^2 = 625 cm^2
H = √(625 cm^2)
H = 25 cm
W = 50 cm
L = 100 cm