The length of Hannah's rectangular living room is 4 meters and the distance between opposite corners is 5 meters. What is the width of Hannah's living room?

To find the width of Hannah's living room, we can use the Pythagorean theorem because a rectangle's diagonal (the distance between opposite corners) forms a right triangle with the length and width of the rectangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:

a² + b² = c²

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

In this case, the length of the hypotenuse is the distance between the opposite corners of the living room, which is 5 meters. The length of the living room is one of the other sides, which is 4 meters. We can call the width of the living room b.

So we can set up the equation as follows:

4² + b² = 5²

Solving for b, we get:

b² = 5² - 4² b² = 25 - 16 b² = 9

Taking the square root of both sides, we find that b = 3.

So, the width of Hannah's living room is 3 meters.