I will give brainliest

In a right angle triangle, there are two sides (i.e. the legs) between which is the right-angle, and the third side of the triangle joins these two sides and is known as the hypotenuse (P.S. always the longest side);

Pythagoras theorem applies to all right-angle triangles and dictates:

The two sides that have the right-angle between them squared will be equivalent to the hypotenuse squared;

Let:

a = one side adjacent to the right-angle

b = the other side adjacent to the right angle

h = hypotenuse

Then:

a² + b² = h²

Considering we have been provided the hypotenuse and one of the legs:

We can plug these values into this equation and solve for the remaining side:

a² + (5)² = (12)²

a² + 25 = 144

a² = 144 - 25

a² = 119

a = √119

6.

This question is a practical example of the Pythagoras theorem in the real world;

The longest length that will exist within the cylindrical can will be from a point along the bottom circumference of the can diagonally, across the diameter, up to the rim of the can on the opposite side;

This will also be the length of the longest nail, or an item of any kind for that matter, that can fit in the can entirely;

The diameter is 4 in;

The height is 6 in;

These two will be the two legs of a right-angle triangle;

The hypotenuse is the solution we want;

Once again:

a² + b² = h²

(4)² + (6)² = h²

16 + 36 = h²

52 = h²

h = √52