Question

in the following figure triangle ABC is a right angled at C and M is the midpoint of hypotenuse AB . If AC =32cm and BC=60cm , then find the length of CM .
the answer is =34cm

Answer 1

using Pythagoras theorem here, we get

AC=68 cm,

since now AD is a median then
AM=BM=AC/2=34 cm,


now using Appoloniaus theorem here to find the length of the median, we have

AC²+BC²=2CM²+2AM²,

32²+60²=2×CM²+2×34²,

1024+3600=2×CM²+2×1156,

4624=2(CM²+1156),

then

CM²+1156=2312,

hence

CM²=2312-1156,

CM²=1156,

therefore

CM=√1156,

CM=√(34×34),

CM=34 cm

Answer 2

Answer:

cm = 34 answer

Step-by-step explanation:

hope it helps