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

It’s wrong

That is wrong!

To find the height of the right triangular prism, we need to use the formula for the volume of a prism:

Volume = Base Area x Height.

First, let's find the area of the triangular base.

Since the base is a right isosceles triangle, we know that the two equal sides measure 25 cm each.

The formula to find the area of a right isosceles triangle is:

Area = (base x height) / 2.

In this case, since the triangle is isosceles, the base and height are equal. Therefore, the formula simplifies to:

Area = (side x side) / 2.

Plugging in the values, we get:

Area = (25 cm x 25 cm) / 2 = 625 cm^2.

Now, we convert the volume from cubic meters to cubic centimeters, since the area is in square centimeters:

0.075 cubic meters = 75000 cubic centimeters.

Now, let's substitute the values into the volume formula:

75000 = 625 cm^2 x Height.

To isolate the height, divide both sides of the equation by 625 cm^2:

Height = 75000 cm^3 / 625 cm^2.

Simplifying the equation yields:

Height = 120 cm.

Therefore, the height of the right triangular prism is 120 cm.

volume=1/3 basearea*h

ok, base area: triangle sides are 25cm each, or .25m
s=semiperimeter
area=s(sqrt(s-side)^3)
s=75/2
s-side=37.5-25=12.5
area=37.5*12.5*sqrt12.5
let E6 mean 10^6
.075E6m=1/3 (37.5*12.5*(sqrt12.5))h
solve for h
I get:137cm
check all this carefully, it is easy to err typing these out.