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Home / Doubts and Solutions/GUJARAT - GUJARATI MEDIUM/Class 9/ગણિત

QID : 67 ­ The perimeters of a square and an equilateral triangle are equal. If the diagonal of the square is 9 cm, what is the area of the equilateral triangle?

Asked by aryap7964 6th December 2017, 4:40 PM
Answered by Expert
Answer:
begin mathsize 16px style Let space the space side space of space straight a space square space be space straight a space and space side space of space an space equilateral space triangle space be space straight s. Now comma space diagonal space of space straight a space square equals 9 space cm rightwards double arrow square root of 2 cross times side space of space straight a space square equals 9 rightwards double arrow square root of 2 straight a equals 9 rightwards double arrow straight a equals fraction numerator 9 over denominator square root of 2 end fraction Now comma space perimeter space of space straight a space square equals perimeter space of space straight a space rectangle rightwards double arrow 4 straight a equals 3 straight s rightwards double arrow straight a equals 3 over 4 straight s rightwards double arrow 3 over 4 straight s equals fraction numerator 9 over denominator square root of 2 end fraction rightwards double arrow straight s equals fraction numerator 9 cross times 4 over denominator 3 cross times square root of 2 end fraction equals 3 cross times 2 cross times square root of 2 equals 6 square root of 2 Thus comma space area space of space an space equilateral space triangle equals fraction numerator square root of 3 over denominator 4 end fraction cross times straight s squared equals fraction numerator square root of 3 over denominator 4 end fraction cross times open parentheses 6 square root of 2 close parentheses squared equals fraction numerator square root of 3 over denominator 4 end fraction cross times 72 equals 18 square root of 3 space sq. space cm end style
Answered by Expert 8th December 2017, 10:07 AM
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