SOLUTION: A rectangular prism has a base who’s length is twice it’s width. The height of the prism is 6in .Find the volume of the prism of the surface area is 208 cm.draw a picture and l

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Question 1155201: A rectangular prism has a base who’s length is twice it’s width. The height of the prism is 6in .Find the volume of the prism of the surface area is 208 cm.draw a picture and label the dimensions given to help set up your problem .
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

 .

Rectangular Prism

h = 6in

l = 2x

w = x

Surface = 2lw + 2lh + 2wh

208 = 2*x*2x + 2*2x*6 + 2*x*6

208 = 4x^2 + 24z + 12x 

52 =  x^2 + 6x + 3x 

x^2 + 9x -52 =0

(x-4)(x+13)=0  x = 4  disposing of negative solution

Volume = Length X Width X Height

V = 8*4*6 = 192in^3 

Wish You the Best in your Studies.