Respuesta :
Answer:
Height: 4 cm
Width: 8 cm.
Length: 12 cm.
Step-by-step explanation:
Let x represent height of the prism.
We have been given that the width is twice the height, so width of the prism would be [tex]2x[/tex].
The length is tree times the height, so length of the prism would be [tex]3x[/tex].
We have been given that a rectangular prism has a volume of 384 cm3. We know that volume of rectangular prism is product of length, width and height. So we can represent our given information in n equation as:
[tex]x\cdot 2x\cdot 3x=384[/tex]
[tex]6x^3=384[/tex]
[tex]\frac{6x^3}{6}=\frac{384}{6}[/tex]
[tex]x^3=64[/tex]
Take cube root of both sides:
[tex]\sqrt[3]{x^3}=\sqrt[3]{64}[/tex]
[tex]x=4[/tex]
Therefore, the height of the prism is 4 cm.
The width of the prism would be [tex]2x\Rightarrow 2(4)=8[/tex].
Therefore, the width of the prism is 8 cm.
The length of the prism would be [tex]3x\Rightarrow 3(4)=12[/tex].
Therefore, the length of the prism is 12 cm.
