l=a, w=a, h=a, d=...?

Question

this is a geometry question on prisms and i can't seem to get past it can someone please explain to me the answer???

Answer 1

The diagonal is the hypotenuse of a right triangle inside the prism with legs a and a sqrt 2

a^2 + (a sqrt 2)^2 = d^2

a^2 + 2a^2 = d^2

3a^2 = d^2

so sqrt (3a^2) = d = a sqrt 3

Answer 2

If D is the distance from opposite corners of the prism (which happens to be a cube) Or D is the Diameter of the sphere that the prism will fit inside, then Just try it has it right = sqrt a cubed.

Answer 3

The diagonal (d) of a rectangular prism is Sqrt(l^2 + w^2+ h^2)
So d = sqrt(a^2 + a^2 +a^2) = sqrt(3a^2) = a*sqrt(3)

Answer 4

Hmm It May not Be Correct.

But Im Thinking
l= length
w= width
h= height
d=depth
l*w*h = area (a)
l*w*h*d = volume (v)
so therefore...

l=a, w=a, h=a, d=v

Its probally not right xD

Answer 5

sqrt(3)*a

diagonal = sqrt(l^2 + w^2 + h^2)