i can not seem to figure this problem out. A piece of cardboard is twice as long

Question

i can not seem to figure this problem out. A piece of cardboard is twice as long as it is wide. itis to be made into a box with an open top by cutting 2 inch squaresfrom each corner and folding up the sides. let X represent thewidth of the original piece of cardboard. Question:For what dimensions of the bottom of the box will thevolume be 320 cubic inches? Determine analytically andgraphically. i can not seem to figure this problem out. A piece of cardboard is twice as long as it is wide. itis to be made into a box with an open top by cutting 2 inch squaresfrom each corner and folding up the sides. let X represent thewidth of the original piece of cardboard. Question:For what dimensions of the bottom of the box will thevolume be 320 cubic inches? Determine analytically andgraphically.

Explanation / Answer

Okay, start this off by saying this: Length=2x Width=x when you cut away from each corner your length is reduced by 2 oneach corner so... Length = 2x-4 Width = x-4 Height will then be 2 so (2x-4)(x-4)(2)=320 4x2-24x+32=320 x2-6x+8=80 x2-6x-72=0 Use calculator to calculate x value: x=12 and x=-6 because you cant have a negative length, height, or width, -6 isdiscarded now plug 12 back into all the formulas L=2x-4=20 W=x-4=8 H=2 20 x 8 x 2 are the dimensions.

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