Question

Seg AM is a median of ΔABC. If AB=22,AC=34,BC=24, find AM

Answer 1

Final Answer: 26 units 

Steps:
1) Since ,AM is median ;
=> BM = MC= BC/2 =24/2 =12 units . 

2) By Apollonius's Theorem, 

[tex]AB^{2} + AC^{2} = 2(AM^{2} + BM^{2}) \\ \\ =\ \textgreater \ 22^{2} + 34^{2} = 2( AM^{2} + 12^{2}) \\ \\ =\ \textgreater \ AM^{2} = \frac{1640}{2}-144=676 \\ \\ =\ \textgreater \ AM = 26 \: units [/tex]

Hence,

$\boxed{AM = 26 \:\:units }$

Answer 2

Answer:

In ABC, AM is a median.

BM=1/2*BC

BM=1/2*24

BM=12cm .

by Apollonius theorem.

${ab}^{2} + {ac}^{2} = 2 \times {am}^{2} + 2 \times {bm}^{2} \\ {22}^{2} + {34}^{2} = 2 \times {am}^{2} + 2 \times {12}^{2} \\ 484 + 1156 = 2 \times {am}^{2} + 2 \times 144 \\ 1640 = 2 \times {am}^{2} + 288 \\ 1640 - 288 = 2 \times {am}^{2} \\ 1352 = 2 \times {am}^{2} \\ \frac{1352}{2} = {am}^{2} \\ 676 = {am }^{2} \\ taking \: square \: root \: \\ 26 = am \\ am = 26cm$