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CBSE Class 9 Answered

If the length of a median of an equilateral triangle is 'x cm', then its area is ________.
Asked by gpnkumar0 | 02 Aug, 2016, 12:07: PM
answered-by-expert Expert Answer
begin mathsize 12px style Median space of space the space equilateral space triangle space equals space space straight x space cm We space know space that space in space an space equilateral space triangle comma space the space median space is space also space the space altitude space left parenthesis that space is comma space height right parenthesis space of space the space triangle. Let space the space side space of space the space triangle space be space straight s. So comma space BD equals straight s over 2 space cm In space right space increment ADB comma AB squared equals BD squared plus AD squared rightwards double arrow straight s squared equals straight s over 4 squared plus straight x squared rightwards double arrow straight x squared equals straight s squared minus straight s over 4 squared rightwards double arrow straight x squared equals fraction numerator 3 straight s over denominator 4 end fraction squared rightwards double arrow straight x equals fraction numerator square root of 3 straight s over denominator 2 end fraction rightwards double arrow straight s equals fraction numerator 2 straight x over denominator square root of 3 end fraction Area space of space increment ABC equals 1 half cross times fraction numerator 2 straight x over denominator square root of 3 end fraction cross times straight x equals fraction numerator straight x squared over denominator square root of 3 end fraction space cm squared end style
Answered by Rebecca Fernandes | 04 Aug, 2016, 10:05: AM

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CBSE 9 - Maths
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