A triangular prism of length 10 cm has a volume of 100 cm^3. If the base is an equilateral triangle, find it's length of side.

Expert Answers

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You need to use the volume equation of triangular prism, such that:

`V = A*h`

`A` represents the area of equilateral triangle that represents the base of prism

`h` represents the height of the prism

You need to evaluate the area of equilateral triangle such that:

`A = (l*l*sin 60^o)/2 => A = l^2*sqrt3/4`

The problem provides the information that the volume of the prism is of `100 cm^3` and the height of prism is of `10 cm` , such that:

`100 = ( l^2*sqrt3/4)*10 => 10 = l^2*sqrt3/4`

`40 = l^2*sqrt3 => l^2 = 40/sqrt 3 => l = sqrt((40sqrt3)/3)`

Hence, evaluating the length of side of equilateral triangle yields `l = sqrt((40sqrt3)/3).`

You need to remember the volume of the triangular prism:

V = Area of the base*height.

The area of the base =

l denotes the length of the side of equilateral triangle and the angle included is of  .

Area of the base = 

The length of the height of the prism is of 10 cm and the volume is of  .

Replacing these values in the formula of volume yields:

 l   4.805 cm

The length of the side of the equilateral base is about l  4.805 cm.

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