Answer:
a. d = [tex]\sqrt{3}[/tex]
b. d = [tex]2\sqrt{3}[/tex]
c. d = [tex]s\sqrt{3}[/tex]
Step-by-step 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 = [tex]\sqrt{x^{2}+x^{2}}=\sqrt{2x^{2} }=x\sqrt{2}[/tex]
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
[tex]d^{2}=(x\sqrt{2} )^{2} + x^{2}=2x^{2} +x^{2} =3x^{2}[/tex]
[tex]d=\sqrt{3x^{2} }=x\sqrt{3}[/tex]
means the length of the side multiply by root 3
a. The length of the side is 1 so [tex]d=\sqrt{3}[/tex]
b. The length of the side is 2 so [tex]d=2\sqrt{3}[/tex]
c. The length of the side is s so [tex]d=s\sqrt{3}[/tex]
