Question

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 54 inches. The width of the rectangle is 27 inches. Which of the following is the perimeter of the inner edge of the frame? (π = 3.14) 192.78 inches 246.78 inches 277.56 inches 331.56 inches

Answer 1

Answer:

The answer is 192.78 inches

Step-by-step explanation:

An oval is formed by a rectangle with semicircles at each end. We can visualize this easily.

The length of the rectangle is 54 inches.

The width of the rectangle is 27 inches.

The perimeter of rectangle is = $2(L+W)$

= $2(54+27)$

= 162 inches

And because there are two semicircles, we can combine them to form a circle. So, perimeter of a circle is called a circumference.

The width of the rectangle forms the diameter, so its half will be the radius.

r = $\frac{27}{2}=13.5$

The circumference is given by : $2\pi r$

= $2\times3.14\times13.5=84.78$ inches

Now as the described oval shape is a complete figure without lines inside, we will subtract the width of both sides of the rectangle from the complete perimeter.

The complete perimeter is = $162+84.78=246.78$ inches

The inner edge perimeter will be = $246.68-2(27)$ = 192.78 inches

Answer 2

It would be 192.78!!!