RRB Group D practice question
The side of a rhombus is 20 cm and one of its diagonals is 24 cm. Find the area of the rhombus.
From a RRB Group D Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (C) 384 sq cm
The diagonals of a rhombus bisect each other at right angles, so half of the given diagonal is 24/2 = 12 cm. By Pythagoras, (side)2 = (12)2 + (half of other diagonal)2, so 202 - 122 = 256, half of other diagonal = 16 cm, so the other diagonal = 32 cm. Area = (1/2) × 24 × 32 = 384 sq cm.
हिंदी में प्रश्न
एक समचतुर्भुज की भुजा 20 सेमी है और उसका एक विकर्ण 24 सेमी है। समचतुर्भुज का क्षेत्रफल ज्ञात कीजिए।
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उत्तर और व्याख्या देखें
सही उत्तर: (C) 384 वर्ग सेमी
समचतुर्भुज के विकर्ण एक-दूसरे को समकोण पर समद्विभाजित करते हैं, अतः दिए गए विकर्ण का आधा भाग 24/2 = 12 सेमी है। पाइथागोरस प्रमेय से, (भुजा)2 = (12)2 + (दूसरे विकर्ण के आधे भाग)2, अतः 202 - 122 = 256, दूसरे विकर्ण का आधा भाग = 16 सेमी, अतः दूसरा विकर्ण = 32 सेमी। क्षेत्रफल = (1/2) × 24 × 32 = 384 वर्ग सेमी।
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