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CBSE Class 10 Answered

A square with perimeter p cm has more area than a circle with circumference p cm. State true or false with explanation
Asked by Trisha Gupta | 07 Oct, 2021, 03:48: PM
Expert Answer
Given: 4a = p and 2pi r = p
rightwards double arrow straight a equals straight p over 4 space space and space straight r equals fraction numerator straight p over denominator 2 straight pi end fraction
Area space of space square space equals space straight a squared equals straight p squared over 16
Area space of space circle space equals space πr squared equals straight pi cross times open parentheses fraction numerator straight p over denominator 2 straight pi end fraction close parentheses squared equals fraction numerator straight p squared over denominator 4 straight pi end fraction equals straight p squared over 4 cross times 7 over 22 equals straight p squared over 16 cross times 28 over 22 equals 1.27 cross times straight p squared over 16
Hence comma space area space of space the space circle space is space greater.
Thus, the statement is "A square with perimeter p cm has more area than a circle with circumference p cm" is false.
Answered by Renu Varma | 07 Oct, 2021, 11:37: PM
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