Question

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

Answer 1

Answer:

a. d = $\sqrt{3}$

b. d = $2\sqrt{3}$

c. d = $s\sqrt{3}$

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 = $\sqrt{x^{2}+x^{2}}=\sqrt{2x^{2} }=x\sqrt{2}$

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

$d^{2}=(x\sqrt{2} )^{2} + x^{2}=2x^{2} +x^{2} =3x^{2}$

$d=\sqrt{3x^{2} }=x\sqrt{3}$

means the length of the side multiply by root 3

a. The length of the side is 1 so $d=\sqrt{3}$

b. The length of the side is 2 so $d=2\sqrt{3}$

c. The length of the side is s  so $d=s\sqrt{3}$