Question

The volume of the triangular prism is 54 cubic units. What is the value of x?

Answer 1

The value of x is 3.....

Answer 2

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,

`V_(Prism)=Area_(Triangle)* Height_(Prism)`

And

`Area_(Triangle)=(1)/(2)* base* Height_(Triangle)`

`=(1)/(2)* 4* x=2x\ unit^2`

Then,

`V_(Prism)=2x* 3x=6x^2`

As the volume is given as 54 unit³, hence

`\Rightarrow 6x^2=54`

`\Rightarrow x^2=9`

`\Rightarrow x=3`

Ignoring -ve values, as length can not be -ve.

Therefore, the value of x is 3 units.