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 60 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) 343.56 inches 289.56 inches 258.78 inches 204.78 inches

PLZZZZZ HALP

Answer 1

The two semicircular ends together form a circle with circumference 2πr where r=27/2=13.5 in.
The two exposed sides of the rectangle contribute 120 inches.
The total perimeter is 120+27π=204.78 in approx, answer option 4.

Answer 2

The perimeter of inner edge of frame is:

204.78 inches.

Explanation:

We are given length(L) of rectangle=60 inches.

Width(W) of rectangle=27 inches.

We know that the inner edge of the frame is comprised of the two length of the rectangle and 2 semicircles.

We know that the width of the rectangle is equal to the diameter of semicircle.

Hence,Radius(r) of semicircle=W/2

= 27/2 inches

Hence, Perimeter of 1 semicircle=π×r

As there are 2 semicircles.

Hence, Perimeter of 2 semicircle=2×π×r

=2×3.14×(27/2)

= 84.78 inches.

Hence, the perimeter of inner edge of frame is:

2×Length of rectangle+Perimeter of 2 semicircle.

= 2×60+84.78

= 204.78 inches.