Mathematics
funny
12

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?

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(1) Answers
NiamhSexton1

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

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