Question
Download Solution PDFOne side of a rhombus is 37 cm and its area is 840 cm2. Find the sum of the lengths of its diagonals.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLet P and Q be the lengths of diagonals of the rhombus,
Area of rhombus = Product of both diagonals/ 2,
⇒ 840 = P × Q /2,
⇒ P × Q = 1680,
Using Pythagorean Theorem we get,
⇒ (P/2)2 + (Q/2)2 = 372
⇒ P2 + Q2 = 1369 ×
4
⇒ P2 + Q2 = 5476
Using perfect square formula we get,
⇒ (P + Q)2 = P2 + 2PQ + Q2
⇒ (P + Q)2 = 5476 + 2 × 1680
⇒ P + Q = 94
Hence option 4 is correct.
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