Help with diagonal and cube???

Question

A diagonal of a cube is 5 multipled sqaure root of 3 inches long.

Find the length of an edge??

How do I do this??

Answer 1

By diagonal I think you ae referring to body diagonal(there's another diagonal, the face dagonal). But anyways,

A cube has all sides equal to each other.
Let's find the face diagonal first. s^2 + s^2 = 2S^2.

Taking the square root gives the face diagonal. i.e (sqrt2)*s
the face diagonal and one of the sides makes a right angle triangle with the body diagonal. i.e,
2S^2 +S^2 = 3S^2. This is the sqaure of the body diagonal.
Therefore the body diagonal is s*sqrt3= 5sqrt3
S*3^1/2 = 5*3^1/2
hence S = 5.

Answer 2

the diagonal of a rectangular solid is given by (l^2+b^2+h^2)^1/2
where l,b and h are the length,breadth and the height.
since in a cube l=b=h=a,where a is the edge of the cube diagonal=(3a^2)^1/2
or a multiplied by square root of 3
.here the diagonal is given equal to 5 multiplied square root of three.
equating
a multiplied square root three=5 multiplied square toot3
giving 'a' the edge of the square as 5"

Answer 3

length of diagonal of cube= (side)* square root of 3 { side means edge}
5* square root of 3 = (side)* square root of 3
5= side { square root of 3 cancels from both sides}
so edge of cube = 5 inches.