To find the perimeter of the inner edge of the frame, we need to add the lengths of the four sides of the inner oval.
First, calculate the circumference of the two semicircles at the ends of the oval. The circumference of a circle is given by the formula: 2πr, where r is the radius. Since we have semicircles, we need to divide the circumference by 2.
The radius of each semicircle is the width of the rectangle, which is 27 inches. Therefore, the circumference of each semicircle is:
C = (2π)(27)/2 = 27π inches
For the length of the oval, it is the same as the length of the rectangle which is 60 inches.
Now, we add up the lengths of the four sides of the inner oval:
Circumference of semicircle + Length of oval + Circumference of semicircle + Width of rectangle
(27π) + 60 + (27π) + 27
= 54π + 87
≈ 289.56 inches
Therefore, the perimeter of the inner edge of the frame is approximately 289.56 inches.
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)
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?
343.56 inches
289.56 inches
258.78 inches
204.78 inches
3 answers
are you sure
I apologize for the mistake in my previous response. Let's correct the calculation.
The perimeter of the inner edge of the frame equals the sum of the lengths of the inner oval's sides.
The lengths of the two straight sides of the oval (top and bottom of the rectangle) are equal to the length of the rectangle, which is 60 inches.
The lengths of the two curved sides of the oval (semicircles) are equal to half the circumference of a circle (since semicircles) with a radius of 27 inches:
Circumference of a circle = 2πr
Circumference of a semicircle = πr
Circumference of each semicircle = π(27) = 27π inches
Adding all four sides:
60 + 60 + 27π + 27π
Therefore, the perimeter of the inner edge of the frame is:
120 + 54π = 120 + 54(3.14) ≈ 318.36 inches
So, the correct perimeter of the inner edge of the frame is approximately 318.36 inches.
The perimeter of the inner edge of the frame equals the sum of the lengths of the inner oval's sides.
The lengths of the two straight sides of the oval (top and bottom of the rectangle) are equal to the length of the rectangle, which is 60 inches.
The lengths of the two curved sides of the oval (semicircles) are equal to half the circumference of a circle (since semicircles) with a radius of 27 inches:
Circumference of a circle = 2πr
Circumference of a semicircle = πr
Circumference of each semicircle = π(27) = 27π inches
Adding all four sides:
60 + 60 + 27π + 27π
Therefore, the perimeter of the inner edge of the frame is:
120 + 54π = 120 + 54(3.14) ≈ 318.36 inches
So, the correct perimeter of the inner edge of the frame is approximately 318.36 inches.
1 answer