Question

A packing company is doing an inventory of boxes. Their most popular box is display below: 2ft,(3x-5)ft,(2x-1)ft you can use the formula V= lwh to find the volume of the box. The volume of the box is 40ft3.What is the value of x ? Find the length and width of the box. Describe any extraneous solutions.

Answer 1

Length of box is(l) =2 ft

width of box is (w) = 3 x - 5 =3(3)-5 = 9-5=4

height of box is (h) = 2 x - 1 =2(3)-1 = 6 -1 =5

Explanation:

Step 1:-

Volume of the box is V= l w h

Given Volume of the box is V = 40 ft^3

given 2 × (3 x-5)×(2 x-1) =40..........(1)

Step 2:-

simplification
`(6 x-10)(2 x-1)=40`

`12 x^(2) -6 x-20 x+10 =40`

`12 x^(2) -20 x -6 x -30=0`

take common 2

`2(6 x^(2) -13 x -15)=0`

Find factors

`6 x^(2) -18 x+5 x-15=0`

`6x(x-3)+5(x-3)=0`

`(6 x+5)(x-3)=0`

x=
`(-5)/(6) and x=3`

Step 3:- The value of x
`(-5)/(6)` is not satisfied

the value of x =3 is satisfied in equation(1)

Therefore the length of the box is l = 2

the width of the box is w = 3 x-5=3(3)-5=9-5=4

The height of the box is h= 2 x-1 = 2 (3) -1 =5

Verification:-

V = 2(4)(5) =40

In the given problem volume is 40 so both are equal

Answer:- The length of the box is l = 2

The width of the box is w =4

The height of the box is h= 5