The volume of a box is 384 cubic inches. the hieght of the box is 4 inches and the length of the box is 4 inches longer than its width. What are the dimensions of the box?
Accepted Solution
A:
Answer:The dimensions are height=4 inches, width=8 inches and lenght=12 inches.Step-by-step explanation:The volumen of a box is:[tex]V=(height*lenght*width)\\[/tex]we don't know the width so let's assume it as x.[tex]V=4*x*(x+4)\\[/tex]that gives us a cuadratic equation:[tex]4x^{2} +16x=384[/tex]let's rerrangage it:∞[tex]4x^{2} +16x-384=0[/tex]we can obtain the value of x using the quadratic formula:[tex]\frac{-b^2\±\sqrt{b^2-4a*c} }{2a}[/tex]that formula gave us two results:[tex]x=8\\x=-12[/tex]we have to take te possitive number, so the width is 8 inches and the length is 8+4=12 inchesheight=4 incheswidth=8 incheslenght=12 inchesVolume=4*8*12=384 cubic inches.