Which of the following quadrilateral ABCD cannot be constructed ?

A.AB = 3, BC = 5, AC = 4, AD = 6, CD = 6

B.AB = 2, BC = 4, AC = 4, AD = 5, CD = 5

C.AB = 3, BC = 5, AC = 6, AD = 3, CD = 2Correct

D.AB = 3, BC = 5, AC = 6, AD = 3, CD = 5

Explanation & Solution

Correct Answer: (C) AB = 3, BC = 5, AC = 6, AD = 3, CD = 2

In geometry, the construction of a quadrilateral is possible only when the sum of the lengths of any two sides is greater than the third side in triangles formed by the diagonals. In option C, for triangle ADC with sides AD = 3, CD = 2, and AC = 6, the sum of two sides (3 + 2 = 5) is less than the third side (6), which violates the triangle inequality theorem making construction impossible.

हिंदी में प्रश्न एवं आदर्श उत्तर

निम्नलिखित चतुर्भुज ABCD में से कौन-सी रचना नहीं की जा सकती ?

A.AB = 3, BC = 5, AC = 4, AD = 6, CD = 6

B.AB = 2, BC = 4, AC = 4, AD = 5, CD = 5

C.AB = 3, BC = 5, AC = 6, AD = 3, CD = 2सही

D.AB = 3, BC = 5, AC = 6, AD = 3, CD = 5

सही उत्तर: (C) AB = 3, BC = 5, AC = 6, AD = 3, CD = 2

ज्यामिति में, किसी चतुर्भुज की रचना तभी संभव है जब त्रिभुज की किन्हीं दो भुजाओं का योग तीसरी भुजा से अधिक हो। विकल्प C में, त्रिभुज ADC की भुजाएँ AD = 3, CD = 2 और AC = 6 हैं, जहाँ दो भुजाओं का योग (3 + 2 = 5) तीसरी भुजा (6) से कम है, जो त्रिभुज की असमानता के नियम का उल्लंघन करता है।

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