Question

A box with no top is to be constructed from a piece of cardboard whose length measures 5 in. more than its width. The box is to be formed by cutting squares that measure 2 in. on each side from the four corners and then folding up the sides. If the volume of the box will be 100 in.cubed​, what are the dimensions of the piece of​ cardboard?

Answer 1

Answer:

$9\text{ inch, }14\text{ inch, }2\text{ inch}$

Step-by-step explanation:

GIVEN: A box with no top is to be constructed from a piece of cardboard whose length measures $5\text{ inch}$ more than its width. The box is to be formed by cutting squares that measure $2\text{ inch}$ on each side from the four corners and then folding up the sides.

TO FIND: If the volume of the box will be $100\text{ inch}^3$​, what are the dimensions of the piece of​ cardboard.

SOLUTION:

Let the width of cardboard be $x$

length of cardboard $=x+5\text{ inch}$

As box is formed by cutting $2\text{ inch }$ squares from corners of cardboard

length of cardboard $=x+5-4=x+1\text{ inch}$

width of cardboard  $=x-4\text{ inch}$

height of cardboard $=2\text{ inch}$

volume of cardboard $=\text{length}\times\text{width}\times\text{height}$

                                   $=2(x+1)(x-4)$

$x^2-3x-54=0$

solving we get

$x=9,-6$

width of cardboard $=9\text{ inch}$

length of cardboard $=x+5=14\text{ inch}$

height of cardboard $=2\text{ inch}$