Question
Download Solution PDFThe length of one side of a rhombus is 41 cm and its area is 720 cm2. What is the sum of the lengths of its diagonals?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFArea of Rhombus = 1/2 × product of diagonals
⇒ 720 = 1/2 × product of diagonals
⇒ Product of diagonals = 1440
(Side of rhombus)2 = (half of one diagonal)2 + (half of the other diagonal)2
⇒ (One diagonal)2 + (Other diagonal)2 = 41 × 41 × 4
(Sum of two diagonal)2 = (One diagonal)2 + (other diagonal)2 + 2 × product of diagonals
⇒ (Sum of two diagonal)2 = 6724 + 2880 = 9604
∴ Sum of two diagonal = 98cmLast updated on Jun 11, 2025
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