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? meters

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) and its width and length form a right triangle. The Pythagorean theorem states that the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (the length and width).

In this case, the length of the diagonal is 5 meters and the length of the room is 4 meters. Let's denote the width as w. According to the Pythagorean theorem, we have:

4^2 + w^2 = 5^2

Solving this equation for w gives us the width of the room.

First, square the given lengths:

16 + w^2 = 25

Next, subtract 16 from both sides of the equation to isolate w^2:

w^2 = 25 - 16 w^2 = 9

Finally, take the square root of both sides to solve for w:

w = √9 w = 3

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