Question

A right triangular prism has a height of 3 ft, a width of 4 ft, and a hypotenuse of 5 ft. The depth of the triangle is missing. If the surface area of the triangular prism is 192 square ft, find the depth of the triangular prism.

What formula would I use to figure this out?

Answer 1

Depth=15
x=(height(h)*width(w)*hypotenuse(y))/2
x=(3*4*5)/2=(60/2)=30
y=(x(x-h)(x-w)(x-y))^(1/2)
f=(-h^4+2(hw)^2+2(wy)^2-w^4+2(hy)^2-y^4)^(1/2)
f=(-3^4+2(3*4)^2+2(4*5)^2-4^4+2(3*5)^2-5^4)^(1/2)
f=576^(1/2)
f=24
Surface Area= 2f(.5)+(h+w+y)*depth
192=depth*(3+4+5)+24(.5)
180=(3+4+5)*depth
180=(12)(depth)
15=depth