Answer-
The value of x is 3 units.
Solution-
Here,
the volume of the prism with triangular base is 54 unit³
The base is a triangle with,
base = 4 units
height = x units
height of the prism = 3x
So, volume of the prism is,
[tex]V_{Prism}=Area_{Triangle}\times Height_{Prism}[/tex]
And
[tex]Area_{Triangle}=\dfrac{1}{2}\times base\times Height_{Triangle}[/tex]
[tex]=\dfrac{1}{2}\times 4\times x=2x\ unit^2[/tex]
Then,
[tex]V_{Prism}=2x\times 3x=6x^2[/tex]
As the volume is given as 54 unit³, hence
[tex]\Rightarrow 6x^2=54[/tex]
[tex]\Rightarrow x^2=9[/tex]
[tex]\Rightarrow x=3[/tex]
Ignoring -ve values, as length can not be -ve.
Therefore, the value of x is 3 units.
