contestada

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters highand have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer thanits width.The volume of a rectangular prism is found using the formula V= / w- h, where / is the length, w is the width, and h is the height.

Andy is designing a dice tray in the shape of a rectangular prism to use during a roleplaying game The tray needs to be three centimeters highand have a volume class=

Respuesta :

Explanation

The volume of a rectangular prism is given by

[tex]v=length\times breadth\times height[/tex]

We have the information:

h =3cm

v=252 cm³

If the width is x

And the length is 5cm longer than the width

L =5+x

Then, we will have

[tex]volume=252=l\times w\times h=(5+x)(x)(3)[/tex]

Thus, we will have

[tex]\begin{gathered} 252=3x(5+x) \\ 252=15x+3x^2 \\ 3x^2+15x-252=0 \end{gathered}[/tex]

Simplifying further

[tex]x^2+5x-84=0[/tex]

Thus, the equation that models the tray will be

[tex]x^2+5x=84[/tex]

Part B

To check if a with of 7.5 is possible, we will put x = 7.5c and check if the equation holds true

[tex](7.5)^2+5(3.5)=93.75[/tex]

since

[tex]\begin{gathered} 93.75\ne84 \\ The\text{ is false} \\ \end{gathered}[/tex]

Therefore, the answer is NO.

It is not possible for the width to be 7.5cm

Otras preguntas