Final answer:
To match the shapes with their approximate perimeters, we calculate the lengths of their sides using the given perimeters and relevant formulas. The triangle has a side length of approximately 3.22 units, the square has a side length of approximately 3.08 units, the circle has a radius of approximately 2.45 units, and the rectangle has a length of approximately 4.13 units.
Step-by-step explanation:
To match the shapes with their approximate perimeters, we need to compare the given values with the formulas for calculating the perimeters of each shape. Let's calculate the perimeters for each shape:
A) Triangle: The formula for the perimeter of a triangle is P = a + b + c, where a, b, and c are the lengths of the sides. Since we have a triangle with an approximate perimeter of 9.66 units, we can assume that it is an equilateral triangle with all sides equal. Therefore, each side will have a length of approximately 9.66/3 = 3.22 units.
B) Square: The formula for the perimeter of a square is P = 4s, where s is the length of one side. We have a square with an approximate perimeter of 12.32 units, so each side will have a length of approximately 12.32/4 = 3.08 units.
C) Circle: The formula for the perimeter of a circle is P = 2πr, where r is the radius. We have a circle with an approximate perimeter of 15.4 units, so we can use the formula to find the radius: 15.4 = 2πr. Divide both sides by 2π to solve for r: r ≈ 15.4/(2π) ≈ 2.45 units.
D) Rectangle: The formula for the perimeter of a rectangle is P = 2(l + w), where l is a length and w is the width. We have a rectangle with an approximate perimeter of 13.16 units. It's not clear from the question whether the given value represents the length or width, so let's assume it is the width. Therefore, the length will be approximately (13.16 - 2w)/2. Substitute the given value for w into the formula to solve for l: 13.16 = 2(l + 2.45). Simplify the equation: l + 2.45 = 6.58. Subtract 2.45 from both sides to solve for l: l ≈ 6.58 - 2.45 ≈ 4.13 units.