Question

In the right angled triangle BAC , AD is an altitude . given that BC=5cm ,CD=1.8 cm ,calculate the value of AB

Answer 1

Correct Question :-

In right angled ΔBAC , AD is an median . given that BC = 5cm ,CD=1.8 cm, calculate the value of AB.

Given :-

• ΔBAC is a right angled triangle.
• AD is an median.
• BC = 5 cm, CD = 1.8 cm

To Find :-

• The value of AB.

Solution :-

⟹ BC = BD + DC (B - D - C)

⟹ 5 = BD + 1.8

⟹ BD = 5 - 1.8

⟹ BD = 3.2 cm

In right angled ΔBAC, AD is an median,

According to geometric mean theorem,

AD² = CD × DB

[ Put the values ]

⟹ AD² = 1.8 × 3.2

⟹ AD² = 5.76

⟹ AD = √5.76

⟹ AD = 2.4 cm

In right angled ΔBDA, ∠BDA = 90°

According to the Pythagoras theorem,

BA² = BD² + DA²

[ Put the values ]

⟹ BA² = 3.2² + 2.4²

⟹ BA² = 10.24 + 5.76

⟹ BA² = 16

⟹ BA = √16

⟹ BA = 4 cm

Therefore,

The value of AB is 4 cm.

Answer 2

Question is given below →

In the right angled triangle BAC , AD is an altitude . given that BC=5cm ,CD=1.8 cm ,calculate the value of AB.

Answer is given below →

Given that →

• ∆BAC is right angled triangle.
• BC = 5 cm , CD = 1.8 cm.
• AD is an median.

To find →

• The value of AB

Solution →

• BC = BD + DC
• 5 = BD + 1.8
• BD = 5 - 1.8
• BD = 3.2 cm

Put the values

• AD² = 1.8 × 3.2
• AD² = 5.76
• AD = √5.76
• AD = 2.4 cm

In right angled ∆BAC , AD is an median,

According to geometric mean theorm,

• AD² = CD × DB

In right angled triangle BDA , Angle BDA = 90°

According to phythagoras theorm,

• BA² = BD² + DA²

Put the values,

• BA² = 3.2² + 2.4²
• BA² = 10.24 + 5.76
• BA² = 16
• BA = √16
• BA = 4

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