Question
Download Solution PDFयदि l, b और p एक आयत की लंबाई, चौड़ाई और परिधि हैं, और b, l और p गुणोत्तर श्रेणी में हैं (क्रम में), तो (l/b)2 है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
l, b और p गुणोत्तर श्रेणी में हैं, जहाँ
l = लंबाई, b = चौड़ाई और p = परिधि
प्रयुक्त अवधारणा:
(a - b)2 = a2 - 2ab + b2
(a + b)2 = a2 + 2ab + b2
आयत की परिधि = 2 × (l + b)
यदि a, b और c गुणोत्तर श्रेणी में हैं (क्रम में) तो,
b2 = ac
स्पष्टीकरण:
प्रश्न के अनुसार
b, l, p गुणोत्तर श्रेणी में हैं
इसलिए, l2 = b × p
⇒ l2 = b × 2(l + b)
⇒ l2 - 2lb = 2b2
⇒ l2 - 2lb + b2 = 2b2 + b2
⇒ (l - b)2 = 3b2
⇒ l - b = √3b
⇒ l = √3b + b
⇒ l = b (√3 + 1)
⇒ l/b = (√3 + 1)/1
⇒ (l/b)2 = (4 + 2√3)/1
∴ l2 : b2 का अनुपात (4 + 2√3) : 1 है।
Last updated on Jul 9, 2025
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