Question

In triangle ABC,AB=AC=10cm.
M is the midpoint of BC,BM=6cm.
a) Find the length of AM.

Answer 1

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Answer 2

Answer: AM = 8 cm.

Step-by-step explanation: In the attached figure, ΔABC is an isosceles triangle, where AB = AC = 10 cm. M is the mid-point of the side BC and BM is drawn. Also given that BM = 6cm.

Now,  in ΔABC ,

since AB = AC, so ∠ABC=∠ACB (angles opposite to equal sides of a triangle are also equal) and AM is the median from A to BC, so BM = CM.

∴ By SAS rule of congruency, ΔABM≅ΔACM.

So, ∠AMB=∠AMC. We also have

∠AMB+∠AMC=180°.

Therefore, ∠AMB=∠AMC=90°, which gives us that ΔAMB is a right angled triangle.

Now, from Pythagoras theorem, we have

AB²  = AM²+ BM²

So,   AM² = AB²-BM²=10²-6²=64=8, thus AM = 8.

Thus, AM = 8 cm.