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.
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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.
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