Question

a right triangle ABC right angled at c what is cm??​

Answer 1

Given:-

• ABC is Right angled ∆.

• AB = 8cm , BC = 6cm

• M is the Mid Point of AB.

To Find:-

• The Value of CM.

Formulae used:-

• Pythogoras Theorem = (h)² = (B)² + (P)²

How to Solve ?

• First we will find the Length of side AB by using Pythogoras theorem

• We will then find out the Side of BM and will show equal to CM

Now,

→ ( h )² = ( B )² + ( P ) ²

→ ( AB )² = ( BC )² + ( AC )²

→ ( h )² = ( 6 )² + ( 8 )²

→ ( h )² = 36 + 64

→ ( h )² = 100

→ √h² = √100

→ h = 10cm

Hence, The Value of AB is 10cm

Atq

→ M is the Mid Point of AB → AM = BM

→ ½ × AB = BM

→ ½ × 10 = BM

→ 5cm = BM

Therefore,

→ CM = BM

→ CM = 5cm

Hence, The Value of CM is 5cm

Answer 2

Answer:

Length of CM = 5 cm

Step-by-step explanation:

For the figure please refer to the attachment

$\red{\boxed{\rm Given}}$

AC = 8cm

CB = 6 cm

M is the mid point of AB,

Therefore,

AM = MB

$\red{\boxed{\rm To \: find}}$

We have to find value of CM

$\red{\boxed{\rm Proof}}$

Construction:- Drop a perpendicular from M on CB and let the point where CB and the perpendicular meets be D

We should know two theorms in order to slove this question which are,

i) Mid point theorem:- Mid point theorem says that line joining the mid points of two sides of a triangle is parallel and is half of the length of the side of the third side.

ii) Converse of Mid point theorem:- If a line is passing through the midpoint of a side and is parallel to the third side then it is also passing through the midpoint of the second side as well.

Here Angle MDB is 90° and Angle ACB is 90°,

We know that if two corresponding angles are equal then we can say that the two lines are parallel

By the above statement,

AC || MD

Using converse of mid point theorem,

As AC and MD are parallel as well as MD is passing through the midpoint of one of the sides,

Therefore,

MD is also passing through the midpoint of CB.

CD = DB = CB/2 = 3 cm.

According to mid point theorem,

As MD is parallel to AC as well as it is passing through midpoints of both the sides,

Therefore,

MD = AC/2 = 4 cm

In ∆MDC,

MC² = MD² + CD²

MC² = 4² + 3² = 16 + 9 = 25

Therefore,

MC = 5 cm

As MC = CM

Therefore,

$\boxed{\rm CM \: = \: 5 \: cm}$