The triangular prism has a volume of 27 cubic units.

A triangular prism.
What will be the volume of the prism if each side is dilated by a factor One-third?
1 cubic unit
3 cubic units
8 cubic units
9 cubic units

Given:

The volume of the triangular prism = 27 cubic units

To find the volume of the prism if each side is dilated by

Formula

The volume of a triangular prism

where, a be the height of the triangle

c be the base of the triangle

h be the height of the prism

Let us take after dilation the we get,

and

So,

After dilation the volume will be

or,

or, [Since, ]

or,

Hence,

After dilation the volume of the prism will be 3 cubic unit.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,