Construct a window in the shape of a semicircle over a rectangle. If the distance around the outside of the window is 8 metres, what dimensions for the rectangle will result in the rectangle having the largest possible area?
A) 1.56 m wide and 2 m tall
B) 1.12 m wide and 2 m tall
C) 2 m wide and 1.5 m tall
D) 1.56 m wide and 1.56 m tall
E) 2 m wide and 1.12 m tall

Question

Quizplus · Accepted Answer

To maximize the area of the rectangle, we need to find the dimensions that satisfy the perimeter constraint. The perimeter of the window is the sum of the rectangle's width, twice its height, and the semicircle's circumference. Solving the equation for the perimeter and maximizing the area gives the rectangle dimensions as 1.56 m wide and 2 m tall.

Construct a Window in the Shape of a Semicircle Over