A rectangular plate measures 3 ft by 4 ft. What is the length of its diagonal?

A rectangular plate measures 3 ft by 4 ft. What is the length of its diagonal?

• A. 3 feet
• B. 4 feet
• C. 5 feet
• D. 7 feet

Answer: (C)

This uses the Pythagorean theorem. The diagonal of a rectangle is the hypotenuse of a right triangle whose legs are the two side lengths. So with sides 3 and 4, the diagonal d satisfies d^2 = 3^2 + 4^2 = 9 + 16 = 25. Therefore d = sqrt(25) = 5. The diagonal is 5 feet. This is the classic 3-4-5 triangle, so the diagonal isn’t equal to a side or to 7, but exactly 5.

This uses the Pythagorean theorem. The diagonal of a rectangle is the hypotenuse of a right triangle whose legs are the two side lengths. So with sides 3 and 4, the diagonal d satisfies d^2 = 3^2 + 4^2 = 9 + 16 = 25. Therefore d = sqrt(25) = 5. The diagonal is 5 feet. This is the classic 3-4-5 triangle, so the diagonal isn’t equal to a side or to 7, but exactly 5.