Mbroswagg
contestada

The length of a rectangular prism is 4√3 units. The height is 3√6 units. If the volume is irrational, which could be the measure of the width of the rectangular prism?
Answer choices:
A. 2√50
B. 4√12
C. 5√8
D. 7√18 PLEASE EXPLAIN ALL STEPS

Respuesta :

volume = length * height * width
             =   4 qrt3 + 3 sqrt6 * w
              = 12 sqrt18 w

let w = 2 sqrt50 then volume =  2*12 *  sqrt 18*50  = 24*30  so this is rational

let w =  4 sqt 12 the v = 48  sqrt12 * sqrt 18 = 48 sqrt30  which is irrational

C and D are rational  
answer is B

The width of the prism is 4√12 and this can be determined by using the formula of the volume of the prism.

Given :

  • The length of a rectangular prism is 4√3 units.
  • The height is 3√6 units.
  • The volume is irrational.

The following steps can be used in order to determine the width of the rectangular prism:

Step 1 - The volume of the prism is given by:

[tex]\rm Volume = L\times H \times W[/tex]

where L is the length, H is the height, and W is the width of the prism.

Step 2 - Now, substitute the values of the known terms in the above formula.

[tex]\rm Volume = 4\sqrt{3} \times 3\sqrt{6} \times W[/tex]

Step 3 - Simplify the above expression.

[tex]\rm Volume = 12\sqrt{18} \times W[/tex]  --- (1)

Step 4 - Now, check all the options by substituting the value of W in the above expression. If it remains rational then that option is correct.

Step 5 - Substitute W = [tex]4\sqrt{12}[/tex] in the expression (1).

[tex]\rm Volume = 12\sqrt{18} \times 4\sqrt{12}[/tex]

[tex]\rm Volume = 48\sqrt{216}[/tex]

Therefore, the correct option is B).

For more information, refer to the link given below:

https://brainly.com/question/1578538

Otras preguntas