he park modeled below consists of a rectangular area and 2 semicircular areas. The area of the rectangular part of the park is 60,000 square yards.
Which of the following is closest to the distance along the perimeter of this park?
1,856 yd
628 yd
914 yd
1,228 yd
To find the perimeter of the park, we need to find the lengths of all four sides of the rectangular part and the circumference of the two semicircular parts.
Let's start by finding the lengths of the sides of the rectangular part:
We are told that the area of the rectangular part is 60,000 square yards, so we can use the formula for the area of a rectangle: Area = Length × Width.
Since the area is given, we can set up the equation: 60,000 = Length × Width.
Since we don't have any information on the width, we cannot determine the exact lengths of the sides.
Next, let's find the circumference of the semicircular parts:
The circumference of a circle is given by the formula Circumference = π × Diameter.
Since we have semicircles, the diameter will be twice the radius.
If the radius is r, then the diameter will be 2r.
The area of a semicircle is given by the formula Area = π × (Radius)^2 / 2.
In this case, the area of each semicircular part is half of the circle since they are semicircles. So we have: Area = π × (Radius)^2 / 2 = π × r^2 / 2.
Now, we know that the rectangular part has an area of 60,000 square yards. Let's assume the width is w and the length is l.
So, w × l = 60,000.
Since we don't have the exact values for w and l, we cannot find the exact perimeter of the park. However, we can estimate the closest value by using the given options.
The closest option is 1,228 yd.