A Wooden Beam Has a Rectangular Cross Section of Height $S = k w h ^ { 2 },$

Multiple Choice

A wooden beam has a rectangular cross section of height h and width w (see figure) . The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 23 inches? Round your answers to two decimal places. [Hint: $S = k w h ^ { 2 },$ where $k > 0$ is the proportionality constant.]

A) w = 13.28 inches and h = 18.78 inches
B) w = 7.67 inches and h = 21.68 inches
C) w = 19.92 inches and h = 11.50 inches
D) w = 16.26 inches and h = 16.27 inches
E) w = 18.78 inches and h = 13.28 inches