A triangular prism has a volume of 75m^3 and a right triangular base of the area of 10m^2.
a) What is the length of the prism?
b) Sketch a possible prism.
Label its dimensions.
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)