Question
Download Solution PDFएक आयत का क्षेत्रफल 300 सेमी2 है और इसके विकर्ण की लंबाई 25 सेमी है। आयत का परिमाप (सेमी में) है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
आयत का क्षेत्रफल = 300 सेमी2
विकर्ण = 25 सेमी
प्रयुक्त सूत्र:
आयत का क्षेत्रफल = लंबाई × चौड़ाई
आयत का परिमाप = 2 (लंबाई + चौड़ाई)
विकर्ण = √(लंबाई2 + चौड़ाई2)
गणना:
प्रश्न के अनुसार,
⇒ लंबाई × चौड़ाई = 300
फिर से,
विकर्ण = √(लंबाई2 + चौड़ाई2)
⇒ √(लंबाई2 + चौड़ाई2) = 25
⇒ √(लंबाई2 + चौड़ाई2) = 625
मान लीजिए लंबाई a है और चौड़ाई b है।
फिर,
⇒ (a + b)2 = a2 + b2 + 2ab
⇒ (a + b)2 = 625 + 2 × 300
⇒ (a + b)2 = 1225
⇒ a + b = 35
आयत का परिमाप = 2(a + b)
⇒ 2 × 35
⇒ 70
∴ आयत का परिमाप 70 है।
Last updated on Jun 11, 2025
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