Question
Download Solution PDFयदि 3x - 4y - 5 = 0 और 3x - 4y + 15 = 0 एक वर्ग की विपरीत भुजाओं के युग्मों का समीकरण है, तो वर्ग का क्षेत्रफल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
रेखा ax + by + c1 = 0 और ax + by + c2 = 0 के बीच की दूरी \(\rm \frac{|c_1-c_2|}{\sqrt{a^2+b^2}}\) है।
वर्ग का क्षेत्रफल = (भुजा)2
गणना:
यहाँ, 3x - 4y - 5 = 0 और 3x - 4y + 15 = 0 एक वर्ग की विपरीत भुजाओं के युग्मों का समीकरण है।
उनके बीच की दूरी =
\(=\frac{|-5-15|}{\sqrt {3^2+4^2}}\\= \frac{20}{\sqrt 25}\\ =\frac{20}{5} \\=4\)
अब वर्ग का क्षेत्रफल = 42 वर्ग इकाई
= 16 वर्ग इकाई
अतः विकल्प (3) सही है।
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