Find the dimensions of the box described. the length is twice as long as the width. the height is 4 inches greater than the width. the volume is 48 cubic inches. find the length, width, height

Width of box= 2inches

Length of box= 4inches

Height of box= 6inches.

Step-by-step explanation:

Let width of box=x inches

Length of box = twice of width==

Height of box= 4 inches greater than width=

Volume of box= 48 cubic inches

We know that the formula of volume of cuboid=

Apply the formula

Volume of box=

Volume of cube =

Apply inspection method to solve the equation

Put

Then we get

Hence, x=0 is not the solution of x

Put x=1 in the equation then we get

Hence x=1 is not the solution of equation.

Put x=2 then we get

8+16-24=0

Hence, x=2 is the solution of equation .

=0

Now substitute equation =0

Sum roots =6

Product of roots=12

When sum of roots  is greater than zero and product of roots is greater than zero then value of roots of equation is imaginary.

Hence, the roots of equation are imaginary.

Lenght , widht and height are dimensions of box therefore, imaginary value are not possible.

Hence, is the only real values of root of equation .Therefore, it is possible and other two imaginary value of roots are not possible .

Widht of box=2 inches

Length of box = =4inches

Height of box==2+4=6 inches

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for