Given:
The side lengths of two cubes are 12 ft and 6 ft.
To find:
The side length of third cube.
Solution:
From the given figure it is clear that the cubes are inclined to each other in such a way so that they form a right angle triangle and side length of third cube is the hypotenuse.
Let x be the side length of the third cube.
Using Pythagoras theorem, we get
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
[tex]x^2=(6)^2+(12)^2[/tex]
[tex]x^2=36+144[/tex]
[tex]x^2=180[/tex]
Taking square root on both sides, we get
[tex]x=\pm\sqrt{180}[/tex]
[tex]x=\pm 6\sqrt{5}[/tex]
Side cannot be negative. So,
[tex]x=6\sqrt{5}[/tex]
Therefore, the side length of the third cube is [tex]x=6\sqrt{5}[/tex] ft.
