Question
Download Solution PDFABDC एक समलम्ब है जिसमें AB || CD है। P और Q क्रमशः AC और BD के मध्यबिंदु हैं। यदि AB = 3 सेमी और CD = 5 सेमी, ABQP के क्षेत्रफल का PQDC के क्षेत्रफल से अनुपात ज्ञात कीजिये।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
AB||CD, AB = 3 सेमी और CD = 5 सेमी
P और Q, AC और BD के मध्यबिंदु हैं ⇒ AP : PC = 1 : 1
उपयोग किया गया सूत्र:
समलम्ब का क्षेत्रफल = 1/2 × समांतर भुजाओं की लंबाई × ऊंचाई,
जहाँ, ऊँचाई = समानांतर पक्षों के बीच की दूरी
गणना:
PQ = ½ [AB + CD]
⇒ ½ [3 + 5] = 4 सेमी
⇒ AP : PC = 1 : 1
⇒ समलम्ब ABQP की ऊँचाई = समलम्ब PQDC की ऊँचाई = h (मान लीजिये)
⇒ ABQP का क्षेत्रफल : PQDC का क्षेत्रफल
⇒ [1/2 × (3 + 4) × h] : [1/2 × (4 + 5) × h]
⇒ 7 : 9
∴ अनुपात 7: 9 है
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