Math, asked by ankitlkadu, 11 months ago

2. D is the midpoint of side BC of triangle ABC. If AB 4.
AC=6 and BC = 8, then find l(AD) and hence
perimeter of triangle ABD.​

Answers

Answered by ArkajyotiM
2

The length of AD is √20cm and the perimeter of ∆ABC is 18cm

Answered by jivya678
4

The value of length of AD = = 2.904 units

The value of Perimeter of Δ ABD =  9.654 unit

Step-by-step explanation:

From the Δ ABD in the figure

AD^{2} = 16 - x^{2} ------ (1)

From the Δ ADC

AD^{2} = 36 - (8  - x)^{2} ---- (2)

From Equation (1) & Equation (2)

16 - x^{2} = 36 - (8 - x)^{2}

16 - x^{2} = 36 - 64 - x^{2} + 16 x

16 = 16 x - 28

16 x = 44

x = 2.75 unit

Thus BD = 2.75 unit

& CD = 8 - 2.75

⇒ CD = 5.25 units

From equation (1)

AD^{2} = 16 - x^{2}

AD^{2} = 16 - 2.75^{2}

AD^{2} = 8.4375\\

AD = 2.904 units

This is the value of length of AD.

Perimeter of Δ ABD = AB + BD + DA

Since AB = 4 , BD = 2.75 &  DA = 2.904

Perimeter of Δ ABD = 4 + 2.75 + 2.904

Perimeter of Δ ABD = 9.654 unit

This is the value of Perimeter of Δ ABD

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