Question

In the following figure $\vartriangle ABC$ is right angled at $C$ and $M$ is the mid point of hypotenuse if $AC = 32cm$ and $BC = 60cm$ , then find the length of $CM$ .
A) $32cm$
B) $30cm$
C) $17cm$
D) $34cm$

Answer 1

Hint: As it is given that ABC is a right angled triangle so we will apply Pythagoras theorem to find the length of AB so is to find the BM and AM because M is the midpoint of the hypotenuse that is BM is equal to AM.

Complete step-by-step answer:
Given: Figure of triangle ABC is given and ABC is a right angled triangle. Two sides AC and BC of triangle are given $32cm$ and $60cm$ respectively. M is mid point of AB.
As triangle ABC is a right angled triangle therefore we will use the theorem of Pythagoras to find the side AB because other two sides AC and BC are given.
According to Pythagoras theorem ; ${H^2} = {B^2} + {P^2}$
Where $H$ represents the hypotenuse that is AB, $B$ represents the base that is BC and $P$ represents the perpendicular that is AC.
Here, $H = AB = ?$
$
  B = BC = 60cm \\
  P = AC = 32cm \\
$
Hence,$\,A{B^2} = {60^2} + {32^2}$
$
  A{B^2} = 3600 + 1024 \\
  A{B^2} = 4624 \\
  AB = \sqrt {4624} \\
  AB = 68cm \\
$
As M is a median vertex from side AB towards C.
Therefore BM=AM=MC .
To find MC we will find BM or AM because it is easy to find BM or AM as we have found the side AB and BM and AM is half the side AB.
Therefore ${\text{BM = AM = }}\dfrac{{{\text{AB}}}}{{\text{2}}}$
Substitute the value of ${\text{AB}}$.
${\text{BM = AM = 34cm}}$
Therefore the the length of ${\text{CM = 34cm}}$

Note: As MC is a median vertex from AB to point C and makes a line in this way that AM=BM=MC, hence we found AM and BM first.