Ben is replacing a door that measures 80 inches by 39 inches. What is the distance between opposite corners of the door?
The door is most likely rectangular, meaning that the angles are all 90 degrees. The distance between the opposite corners are the diagonals of the rectangle, which has base length 39 and height 80 (can be used interchangebly). By the pythagorean theorem, the hypotenuse/diagonal squared = width^2 + length^2. So diagonal^2 = 80^2 + 39^2 = 7921. Square root both sides and you get 89.
The distance between the opposite corners of the door is 89 inches.