SOLUTION: The length of rectangular solids is four times the width and the height is twice the width. Find the volume and the length of its diagonal if the total surface area is 198 in2

Let W be the width. 

Then the length is 4W and the height is 2W.


The total surface area is  2*(LW + LH + WH) = 2*( (4W)*W + (4W)*(2W) + W*(2W) ) = 2*(4W^2 + 8W^2 + 2W^2) = 28W^2.


Thus we have this equation to determine W


    28W^2 = 198 in^2.


It implies


    W^2 = 198/28 =  = .

    W            = .


Thus the dimensions are:  the length is  L = ;  the width  W = ;  the height  H = .


The 3D diagonal of the solid is  D^2 = L^2 + W^2 + H^2 =  = ;   D =  =   in^2.    ANSWER


The volume is  LWH =  =   in^3.      ANSWER