Can you solve this one problem

The volume of a right prism with an altitude of 15 m and having an equilateral triangle as its base is equal to 234 m3. Determine the length of the side of the triangular base.

The volume of a prism = Bh, with B = the area of the base, h = height of the prism.

In your problem, 234 = B(15), so divide both sides by 15 to get B, and you get B = 15.6.

B in this case is a triangle, and the formula for area of a triangle is 1/2bh. In an equilateral triangle, the height is b(sqrt3)/2. so 15.6 = 1/2(b)(b(sqrt3)/2)

15.6 = b^2(sqrt3)/4 Clear the fraction by multiplying both sides by 4

62.4 = b^2(sqrt3) divide both sides by sqrt 3

36.02 = b^2 square root both sides

6 = b approximately

Hope this helps.

Here,height=15m
Volume=234 m^3
=> Area of base= Volume/ height
=234/15
=15.6 m^2

We have area of equilateral triangle=[3^(0.5)s^2]/4

=>15.6=[3^(0.5)s^2]/4
=> 3^(0.5)s^2]=15.6*4=62.4
=>s= square root of [62.4/ 3^(0.5)]=6.0022m Ans

S² √3
-------- * h = V
4
S²√3
------ * 15 = 234
. 4

S² √3 = 936

S² = 936 /√3.................Multiply by √3 / √3

S² = 936√3 / 3

S² = 312 √3

S = √(312√3)cm

S ~ 23.25cm