A building with square corners has outside measurements of 12 feet by 16 feet. What is the diagonal measurement?

A building with square corners has outside measurements of 12 feet by 16 feet. What is the diagonal measurement?

• A. 27 ft
• B. 25 ft
• C. 20 ft
• D. 18 ft

Answer: (C)

In a rectangle, the diagonal forms the hypotenuse of the right triangle whose legs are the two side lengths. Use the Pythagorean theorem: diagonal^2 = 12^2 + 16^2 = 144 + 256 = 400. The diagonal is sqrt(400) = 20. So the diagonal measures 20 feet. This matches the familiar 12-16-20 right triangle. The other values would not satisfy the Pythagorean sum with these sides (for example, 27^2, 25^2, or 18^2 do not equal 12^2 + 16^2).

In a rectangle, the diagonal forms the hypotenuse of the right triangle whose legs are the two side lengths. Use the Pythagorean theorem: diagonal^2 = 12^2 + 16^2 = 144 + 256 = 400. The diagonal is sqrt(400) = 20. So the diagonal measures 20 feet. This matches the familiar 12-16-20 right triangle. The other values would not satisfy the Pythagorean sum with these sides (for example, 27^2, 25^2, or 18^2 do not equal 12^2 + 16^2).