Given:
The side lengths of two cubes are 2.5 yd and 2 yd.
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 base.
Let x be the side length of the third cube.
Using Pythagoras theorem, we get
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
[tex](2.5)^2=(x)^2+(2)^2[/tex]
[tex]6.25=x^2+4[/tex]
[tex]6.25-4=x^2[/tex]
[tex]2.25=x^2[/tex]
Taking square root on both sides, we get
[tex]x=\pm\sqrt{2.25}[/tex]
[tex]x=\pm 1.5[/tex]
Side cannot be negative. So,
[tex]x=1.5[/tex]
Therefore, the side length of the third cube is [tex]x=1.5[/tex] yd.
