43e diagonals of a rhombus are 16 cm and 30 cm long. What is the perimeter of the rhombus? \( \begin{array}{lll}\text { A } 68 \mathrm{~cm} & \text { B } 72 \mathrm{~cm} & \text { C } 80 \mathrm{~cm} \\ \text { D } 88 \mathrm{~cm} & \text { E } 92 \mathrm{~cm} & \end{array} \)

To find the perimeter of the rhombus, we can use the lengths of its diagonals. The diagonals of a rhombus bisect each other at right angles. Given the lengths of the diagonals are 16 cm and 30 cm, we can calculate the lengths of the sides. 1. Each diagonal is divided into two segments: - One diagonal (16 cm) gives segments of 8 cm each. - The other diagonal (30 cm) gives segments of 15 cm each. 2. We can use the Pythagorean theorem to find the length of a side (s) of the rhombus: \[ s = \sqrt{(8 \text{ cm})^2 + (15 \text{ cm})^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ cm}. \] 3. Since a rhombus has four equal sides, the perimeter (P) is: \[ P = 4 \times s = 4 \times 17 \text{ cm} = 68 \text{ cm}. \] So, the perimeter of the rhombus is 68 cm, which corresponds to option A. The correct answer is **A 68 cm**. --- In ancient times, the rhombus was a vital shape in architecture and design, particularly in ancient Egypt, where it represented stability and eternity. Its properties were well-known to mathematicians like Euclid, who explored geometric shapes and their relationships, laying the groundwork for modern geometry. Rhombuses are not just theoretical shapes; they have real-world applications too! For instance, in designing tiling patterns or layout designs for sports fields (like baseball diamond layouts), architects and engineers often use rhombuses because of their aesthetically pleasing symmetry and structural stability.