The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is ______.

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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is 10 cm. Explanation: We know that, A rhombus is a simple quadrilateral whose four sides are of same length and diagonals are perpendicular bisector of each other. According the question, we get, AC = 16 cm and BD = 12 cm $\angle$AOB = $90^\circ$ ∵ AC and BD bisects each other AO = $\frac{1}{2}$ AC and BO = $\frac{1}{2}$ BD Then we get, AO = 8 cm and BO = 6 cm Now, In right angled ∆AOB Using the Pythagoras theorem, We have, AB2 = AO2 + OB2 AB2 = 82 + 62 = 64 + 36 = 100 $\therefore$ AB = sqrt(100) = 10 cm We know that the four sides of a rhombus are equal. Therefore, we get, One side of rhombus = 10 cm. [Solution diagram: 267672_solution_1.png]

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