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.



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sciencesolve's profile pic

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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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neela's profile pic

Posted on

Area of an equilateral triangle with side a is [(sqrt3)a^2]/4.

The volume of prism with base area A and height h =base area*height. Height (or length) is given = 10cm

Therefore, the volume, v={[ (sqrt3)a^2]/4 }10 which is equal to 100cm^3.Solve for a from this equality.

(sqrt3)a^2 = 100*4/10.

a^2= sqrt(10*4/sqrt3)=sqrt(40/(sqrt(3) )=                =4.8056 cm approximately.

Threfore, the length of the sides of the equilateral triangle is 4.8056cm approximately.

deviselva75's profile pic

Posted on

length of its side is 4.472.the formula used is 0.5xbhl

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