The floor of a rectangular living room is 15 feet by 36 feet. What is the distance between opposite corners of the living room?

To find the distance between opposite corners of the room, we can use the Pythagorean theorem, which 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.

Here, the length and width of the room form the two sides of a right triangle, and the distance between the opposite corners is the hypotenuse.

Step 1: Square the length of the room. 15^2 = 225 square feet.

Step 2: Square the width of the room. 36^2 = 1296 square feet.

Step 3: Add the squares of the length and width. 225 + 1296 = 1521 square feet.

Step 4: Take the square root of the sum to find the length of the hypotenuse. The square root of 1521 is 39.

So, the distance between the opposite corners of the room is 39 feet.