A rectangular cardboard sheet has a length that is 1.5 times greater than the width. Is it possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet if squares with a side of 8 cm are cut from the corners? Find the dimensions of the cardboard sheet.

Answer:Yes, it is possible  to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.The dimensions of the cardboard sheet are 54 cm x 36 cmStep-by-step explanation:Letx ----> the length of the cardboard sheety ----> the width of the cardboard sheetwe know that[tex]x=1.5y[/tex] ----> equation AThe volume of the topless box is[tex]V=LWH[/tex]where[tex]V=6,080\ cm^3[/tex][tex]L=x-2(8)=(x-16)\ cm[/tex][tex]W=y-2(8)=(y-16)\ cm[/tex][tex]H=8\ cm[/tex]substitute[tex]6,080=(x-16)(y-16)8[/tex] ----> equation Bsubstitute equation A in equation B[tex]6,080=(1.5y-16)(y-16)8[/tex] [tex]6,080/8=(1.5y-16)(y-16)[/tex] [tex]760=1.5y^2-24y-16y+256[/tex] [tex]760=1.5y^2-40y+256[/tex] [tex]1.5y^2-40y+256-760=0[/tex] [tex]1.5y^2-40y-504=0[/tex] Solve for ySolve the quadratic equation by graphingThe solution is y=36 cmsee the attached figureFind the value of x[tex]x=1.5y[/tex] ----> [tex]x=1.5(36)=54\ cm[/tex]thereforeYes, it is possible  to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.The dimensions of the cardboard sheet are 54 cm x 36 cm