Question

A triangular prism has an isosceles right triangle as a base. The volume of the prism is 342.1 cm3. Find the measure of one of the legs of the base if the height of the prism is 13.2 cm. Round to the nearest tenth.
3.6 cm
7.2 cm
5.1 cm
6.2 cm

Answer 1

The triangle has sides "a", "b" and "c", where side a = side b and the hypotenuse (side "c") equals side "a" or "b" times the square root of 2.

Prism volume = triangle area * height
342.1 = triangle area * 13.2
triangle area =  342.1 / 13.2
triangle area =  25.9166666667

area of a triangle is (1/2) base * height
In a 45 45 90 triangle, the base = height and since we don't know either the base or the height we'll call both "x".
So triangle area = (1/2) * x^2
25.9166666667 = (1/2) * x^2
x^2 = 51.8333333334
x ( the base and the height) = 7.1995370222  
the hypotenuse of a 45 45 90 triangle = leg * square root (2) =
hypotenuse = 7.1995370222 * sq root (2)
hypotenuse = 10.1816828995

So, one of the legs = 7.1995370222

Source:
http://www.1728.org/triprism.htm