Peters luggage is a rectangular prism has a volume of 834 cm a length of 1.2 cm a width of 2 cm in a height of M centimeters what is the value for M

To find the value of 'M', which represents the height of Peter's luggage (a rectangular prism), we can use the formula for the volume of a rectangular prism. The formula to calculate volume 'V' is given by:

[tex]\boxed{ \begin{array}{ccc} \text{\underline{Volume of a Rectangular Prism:}} \\\\ V = lwh \\\\ \text{Where:} \\ \bullet \ V \ \text{is the volume} \\ \bullet \ l \ \text{is the length} \\ \bullet \ w \ \text{is the width} \\ \bullet \ h \ \text{is the height} \end{array}}[/tex]

We are given:

V = 834 cm³
l = 1.2 cm
w = 2 cm
h = M

We can rearrange the formula to solve for the height (M):

[tex]\Longrightarrow V=lwM\\\\\\\\\therefore M = \dfrac{V}{lw}[/tex]

Plug our given values in and solve for 'M':

[tex]\Longrightarrow M = \dfrac{834 \text{ cm}^3}{(1.2 \text{ cm})(2 \text{ cm})}\\\\\\\\\Longrightarrow M = \dfrac{834 \text{ cm}^3}{2.4 \text{ cm}^2}\\\\\\\\\therefore M = \boxed{347.5 \text{ cm}}[/tex]

Thus, the height of Peter's luggage, a rectangular prism, is 347.5 centimeters.