Question
Download Solution PDFएक समांतर चतुर्भुज की भुजाएँ 3x + 2 और 5x + 4 हैं। इसका परिमाप 44 सेमी और क्षेत्रफल 64 सेमी2 है। इसकी भुजाओं के बीच न्यून कोण का मान डिग्री में क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
एक समांतर चतुर्भुज की भुजाएँ = 3x + 2 और 5x + 4
परिमाप = 44 सेमी और क्षेत्रफल = 64 सेमी2
प्रयुक्त सूत्र:
समांतर चतुर्भुज का परिमाप = 2 (भुजा + आधार)
हल:
⇒ परिमाप = 2(3x + 2) + 2(5x + 4)
⇒ 44 = 2(3x + 2) + 2(5x + 4)
⇒ 44 = 6x + 4 + 10x + 8
⇒ 16x = 32
⇒ x = 2
इसलिए समांतर चतुर्भुज की भुजाएँ इस प्रकार हैं:
⇒ 3x + 2 = 8
⇒ 5x + 4 = 14
त्रिभुज का क्षेत्रफल = 1/2 × समांतर चतुर्भुज का क्षेत्रफल
⇒ 1 / 2 × 8 × 14 × sinθ = 64 / 2
⇒ sinθ = 0.571
हम जानते हैं कि, sin 30° = 1/2 = 0.5 और sin 60° = √3 / 2 = 1.73/2 = 0.865
साथ ही, sin का मान 90° तक बढ़ जाता है और उसके बाद घट जाता है।
अतः, सही उत्तर विकल्प 4 है।
Last updated on Jun 27, 2025
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