VOLUME

the length is 7.5m

dimensions of the base (and the top) are:  4m, 5m, √41m 

First here is a sketch of a right triangular prism:

The triangular end has an area of 10 m²  as given

   area * length = volume

    10  * L = 75 m³

        L = 7.5 m                  

Now find appropo dimensions which will give triangle area of 10 m²

           area = 1/2 b * h

             10 = 1/2 b h

              20 = bh                     so b and h have to multiply to 20      easy ones would be   4 and 5  

                                                         but you could pick ANYthing that multiplies to 20       10   and 2     or   6 and 3 1/3    etc

                                                  whatever you pick for b and h    the hypotenuse dimension will be found by Pythagorean theorem

                                                           4^2 + 5^2 = h^2         h = sqrt 41

So your sketch would look like this (if you use 4 5 sqrt 41)

Thanks Guys :)

The most important thing to understand here is that

For ANY right prism, the volume is the area of the front face multiplied by how far back it goes.

Volume of prism = Area of front * depth

so in this case

75=10*?