You have fifty feet of fencing to use to create a new pen for your dog. Describe three differently-shaped pens you could create.
square - 12.5 feet on each side
rectangle - ??
equilateral triangle - 16 2/3 feet on each side
To describe three differently-shaped pens with fifty feet of fencing, let's consider the following shapes: square, rectangular, and circular.
1. Square Pen:
A square pen has four equal sides. To determine the dimensions of the pen, divide the total fencing length by 4 since all sides are equal. In this case, 50/4 = 12.5 feet. Thus, a square pen with a perimeter of 50 feet would have each side measuring 12.5 feet.
2. Rectangular Pen:
A rectangular pen has two pairs of equal sides. To calculate the dimensions, divide the total fencing length by 2 to find the length of the shorter sides. In this case, 50/2 = 25 feet. Let's consider one side as 25 feet and try to find the length of the other side. Since we have two short sides and two long sides, subtract twice the length of one side from the total fencing length: 50 - 2 * 25 = 0. Thus, it is impossible to create a rectangular pen with a perimeter of 50 feet.
3. Circular Pen:
A circular pen has a curved shape. The perimeter of a circle is given by the formula 2 * π * r, where r is the radius. In this case, the perimeter is 50 feet. To find the radius, divide the total perimeter by 2π: 50 / (2 * π) ≈ 7.96 feet. Therefore, a circular pen could be created with a radius of approximately 7.96 feet.
So, with 50 feet of fencing, you can create a square pen with equal sides measuring 12.5 feet, or a circular pen with a radius of approximately 7.96 feet.