Question

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Answer 1

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

$Hypotenuse^2=Base^2+Perpendicular^2$

$x^2=(6)^2+(12)^2$

$x^2=36+144$

$x^2=180$

Taking square root on both sides, we get

$x=\pm\sqrt{180}$

$x=\pm 6\sqrt{5}$

Side cannot be negative. So,

$x=6\sqrt{5}$

Therefore, the side length of the  third cube is $x=6\sqrt{5}$ ft.