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ICSE Class 9 Answered

in right angled tringleprove thatfour times the sum of the squareson the medians drawn from the acute anglesis equal tofive timesthe square on the hypotensues. 
Asked by japooyani | 02 Aug, 2018, 08:32: AM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove space colon space 4 left parenthesis BM squared space plus space CN squared right parenthesis space equals space BC squared Here space AN space equals space BN space equals space AB over 2 space and space space AM space equals CM space equals space AC over 2 space space space.... left parenthesis 1 right parenthesis By space Pythagoras space Theoren space in space increment ABC comma space we space get BC squared space equals space AB to the power of 2 space end exponent plus space AC squared space space space space space..... left parenthesis 2 right parenthesis By space Pythagoras space Theoren space in space increment ACN comma space we space get CN squared space equals space AC squared space plus space AN squared space space space space space space space space space space space space space.... from left parenthesis 1 right parenthesis rightwards double arrow CN squared space equals space AC squared space plus space open parentheses AB over 2 close parentheses squared rightwards double arrow CN squared space equals space AC squared space plus space AB squared over 4 rightwards double arrow 4 CN squared space equals space 4 AC squared space plus space AB squared space space space space space space space space space...... left parenthesis 3 right parenthesis By space Pythagoras space Theorem space in space increment AMB comma space we space get BM squared space equals space AB squared space plus space AM squared space space space space space space space space space space space space space.... from left parenthesis 1 right parenthesis rightwards double arrow BM squared space equals space AB squared space plus space open parentheses AC over 2 close parentheses squared rightwards double arrow BM squared space equals space AB squared space plus space AC squared over 4 rightwards double arrow 4 BM squared space equals space 4 AB squared space plus space AC squared space space space space space space space space space...... left parenthesis 4 right parenthesis space space space space space space space Adding space left parenthesis 3 right parenthesis space and space left parenthesis 4 right parenthesis comma space we space get 4 CN squared space plus space 4 BM squared equals space 5 AC squared space plus space 5 AB squared space space space 4 left parenthesis BM squared space plus CN squared right parenthesis space equals 5 left parenthesis AC squared space plus space AB squared right parenthesis space...... from left parenthesis 2 right parenthesis 4 left parenthesis BM squared space plus CN squared right parenthesis space equals 5 BC squared space space space space Hence space proved. end style
Answered by Yasmeen Khan | 02 Aug, 2018, 09:46: AM

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