Question

Num 27. Please answer and explain if you have time but totally not needed

Answer 1

a. d =
`√(3)`

b. d =
`2√(3)`

c. d =
`s√(3)`

Explanation:

to find the length of the longest diagonal of the cube at first you will find the length of the diagonal if its base

If the length of the side of a cube is x

∴the length of the diagonal of the base =
`\sqrt{x^(2)+x^(2)}=\sqrt{2x^(2) }=x√(2)`

Now to find the length of the longest diagonal we will use Pythagoras with the side of the cube and the diagonal of the base

`d^(2)=(x√(2) )^(2) + x^(2)=2x^(2) +x^(2) =3x^(2)`

`d=\sqrt{3x^(2) }=x√(3)`

means the length of the side multiply by root 3

a. The length of the side is 1 so
`d=√(3)`

b. The length of the side is 2 so
`d=2√(3)`

c. The length of the side is s so
`d=s√(3)`