Question

The opening in a rectangular door frame measures 9 feet by 3 feet. Each of the four doors described in the table measures 9

feet by 3 feet, but have different diagonal lengths. Which door will fit in the rectangular opening?
Door 1
Door 2
diagonal: 10 feet
Door 3
diagonal 3 V10 feet
Door 4
diagonal: 6
feet
diagonal: 12 feet
Door 1
Door 2
Door 3
Door

Answer 1

Door 2

Explanation:

Answer 2

Door 3 diagonal 3√10 feet

Explanation:

The diagonal of a rectangle is the hypotenuse of a right triangle whose legs are the side lengths of the rectangle. That is, the diagonal of a 9 ft by 3 ft rectangle will have length ...

d = √(9² +3²) = √90 = 3√10

Any "9 ft by 3 ft" figure that has a diagonal different from this is not a rectangle. To fit the rectangular opening, we want a rectangular door—one with a diagonal of 3√10 feet.