Question
Download Solution PDFएका समांतरभुज चौकोनाच्या बाजू 3x + 2 आणि 5x + 4 आहेत. त्याची परिमिती 44 सेमी आणि क्षेत्रफळ 64 सेमी2 आहे. तर अंशांमध्ये त्याच्या बाजूंमधील लघुकोनाचे मूल्य किती असेल?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
समांतरभुज चौकोनाच्या बाजू = 3x + 2 आणि 5x + 4
परिमिती = 44 सेमी आणि क्षेत्रफळ = 64 सेमी2
वापरलेले सूत्र:
समांतरभुज चौकोनाची परिमिती = 2 (बाजू + पाया)
स्पष्टीकरण:
⇒ परिमिती = 2(3x + 2) + 2(5x + 4)
⇒ 44 = 2(3x + 2) + 2(5x + 4)
⇒ 44 = 6x + 4 + 10x + 8
⇒ 16x = 32
⇒ x = 2
म्हणून समांतरभुज चौकोनाच्या बाजू,
⇒ 3x + 2 = 8
⇒ 5x + 4 = 14
त्रिकोणाचे क्षेत्रफळ = 1/2 × समांतरभुज चौकोनाचे क्षेत्रफळ
⇒ 1 / 2 × 8 × 14 × sinθ = 64 / 2
⇒ sinθ = 0.571
आपल्याला माहित आहे की, sin 30° = 1/2 = 0.5 आणि sin 60° = √3 / 2 = 1.73/2 = 0.865
तसेच, sin चे मूल्य 90° पर्यंत वाढते आणि त्यानंतर ते कमी होते.
त्यामुळे पर्याय 4 योग्य आहे.
Last updated on Jun 27, 2025
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