Subjects geometry

Perimeters Circumference F755D7

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1. The problem involves calculating perimeters or circumferences based on given dimensions. 2. The formulas for each shape are: - Square's perimeter: $$P = 4s$$ where $s$ is the side length. - Circle's circumference: $$C = 2\pi r$$ where $r$ is the radius. - Parallelogram's perimeter: $$P = 2(a + b)$$ where $a$ and $b$ are the lengths of adjacent sides. 3. Given values: 28 square inches (likely area of square), 3.5 (possibly side length or radius), 20/3, and 25/6 (likely side lengths). 4. For the square, if area $A = 28$, then side length $s = \sqrt{28} = 2\sqrt{7}$. 5. Square's perimeter: $$P = 4s = 4 \times 2\sqrt{7} = 8\sqrt{7}$$ inches. 6. For the circle, if radius $r = 3.5$, circumference: $$C = 2\pi \times 3.5 = 7\pi$$ inches. 7. For the parallelogram, sides $a = \frac{20}{3}$ and $b = \frac{25}{6}$. 8. Parallelogram's perimeter: $$P = 2\left(\frac{20}{3} + \frac{25}{6}\right) = 2\left(\frac{40}{6} + \frac{25}{6}\right) = 2 \times \frac{65}{6} = \frac{130}{6} = \frac{65}{3}$$ inches. 9. Final answers: - Square's perimeter: $8\sqrt{7}$ inches. - Circle's circumference: $7\pi$ inches. - Parallelogram's perimeter: $\frac{65}{3}$ inches.