A cube had side lengths of 3cm. Find the length of the diagonal of the cube

Question

Answer 

Answer 1

draw a cube

draw the diagonal of the bottom square

the diagonal of the bottom square forms an isosceles right triangle

the length of the hypotenuse is always x√2 where x=side length which is 3 cm

therefore the diagonal is 3√2 cm

draw the diagonal of the cube

this forms a right triangle whose legs are 3√2 which we just found and 3, a side of the cube

use the Pythagorean Theorem

d=diagonal of the cube

d²=(3√2)²+3²

d²=18+9

d²=27

take the square root of each side

d=√27

d=3√3 cm (or 3*1.732=5.196 cm)