Respuesta :
Answer:
[tex]9\text{ inch, }14\text{ inch, }2\text{ inch}[/tex]
Step-by-step explanation:
GIVEN: A box with no top is to be constructed from a piece of cardboard whose length measures [tex]5\text{ inch}[/tex] more than its width. The box is to be formed by cutting squares that measure [tex]2\text{ inch}[/tex] on each side from the four corners and then folding up the sides.
TO FIND: If the volume of the box will be [tex]100\text{ inch}^3[/tex], what are the dimensions of the piece of cardboard.
SOLUTION:
Let the width of cardboard be [tex]x[/tex]
length of cardboard [tex]=x+5\text{ inch}[/tex]
As box is formed by cutting [tex]2\text{ inch }[/tex] squares from corners of cardboard
length of cardboard [tex]=x+5-4=x+1\text{ inch}[/tex]
width of cardboard [tex]=x-4\text{ inch}[/tex]
height of cardboard [tex]=2\text{ inch}[/tex]
volume of cardboard [tex]=\text{length}\times\text{width}\times\text{height}[/tex]
[tex]=2(x+1)(x-4)[/tex]
[tex]x^2-3x-54=0[/tex]
solving we get
[tex]x=9,-6[/tex]
width of cardboard [tex]=9\text{ inch}[/tex]
length of cardboard [tex]=x+5=14\text{ inch}[/tex]
height of cardboard [tex]=2\text{ inch}[/tex]
