A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: An oval is formed by a rectangle
with semicircles at each end. The length of the rectangle is 60 inches. The width of the rectangle is 27 inches. Which of the following is the perimeter of the inner edge of the frame?
We can solve this by first finding the diameter of the two semicircles. We know that the width of the rectangle is 27 inches, which also happens to be the diameter of the circle.
The circumference of a circle is 2πr or πd. The problem says that it is a semicircle, however, it says that there are two of them. Since the two semicircles are the same size, we know that they can combine to form one circle, so we can just find the circumference of one circle to account for both of the semicircles:
C=27π inches
We also know that the length of the rectangle is 60 inches. We only want to find the perimeter of the frame, so we don't have to account for the widths of the rectangle because it is inside the frame. Therefore, the two sides of the rectangle together are 120 inches. Now we can add this to the circumference we found:
120+27π inches or 204.78 inches (depends on what your teacher is asking for)
