Okay, so I'm having trouble answering this math problem. Here we go:
The base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm each. The volume of the prism is 0.075 cubic meters. Find the height of the prism.
The volume of any prism can be calculated using the formula
`V = h*B` , where h is the height of the prism and B is the area of the prism.
In this problem, the base is a right isosceles triangle. The area of such triangle will be `B = 1/2 a^2` , where a is the length of the equal sides. So in our case, the volume of the prism will be
`V = 1/2 ha^2`
Since the length of the equal sides is given in centimeters, but the volume of the prism is given in cubic meters, convert the value of a to meters before plugging it in:
a = 25 cm = 0.25 m.
Now we can plug in values of V and a into the formula above:
`0.075 m^3 = 1/2 h*(0.25)^2 m^2`
Multiplying both sides by 2 results in
0.15 m^3 = h*0.0625 m^2
From here, h can be found by dividing both sides by 0.0625:
`h=0.15/0.0625 m = 2.4 m`
The height of the given prism is 2.4 meters.