If the length of a median of an equilateral triangle is 'x cm', then its area is ________.

Asked by gpnkumar0 | 2nd Aug, 2016, 12:07: PM

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 | 4th Aug, 2016, 10:05: AM