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Home » 1. In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. (v) if         and     find AB.(vi) if         and     find BC.
1. In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. (v) if

    \[\mathbf{AC}\text{ }=\text{ }\mathbf{4}.\mathbf{2}\text{ }\mathbf{cm},\]

    \[\mathbf{DC}\text{ }=\text{ }\mathbf{6}\text{ }\mathbf{cm},\]

and

    \[\mathbf{BC}\text{ }=\text{ }\mathbf{10}\text{ }\mathbf{cm},\]

find AB.(vi) if

    \[\mathbf{AB}\text{ }=\text{ }\mathbf{5}.\mathbf{6}\text{ }\mathbf{cm},\]

    \[\mathbf{AC}\text{ }=\text{ }\mathbf{6}\text{ }\mathbf{cm},\]

and

    \[\mathbf{DC}\text{ }=\text{ }\mathbf{3}\text{ }\mathbf{cm},\]

find BC.
CBSE | Class 10 | Exercise 4.3 | Maths | RD Sharma | Triangles
1. In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. (v) if

    \[\mathbf{AC}\text{ }=\text{ }\mathbf{4}.\mathbf{2}\text{ }\mathbf{cm},\]

    \[\mathbf{DC}\text{ }=\text{ }\mathbf{6}\text{ }\mathbf{cm},\]

and

    \[\mathbf{BC}\text{ }=\text{ }\mathbf{10}\text{ }\mathbf{cm},\]

find AB.(vi) if

    \[\mathbf{AB}\text{ }=\text{ }\mathbf{5}.\mathbf{6}\text{ }\mathbf{cm},\]

    \[\mathbf{AC}\text{ }=\text{ }\mathbf{6}\text{ }\mathbf{cm},\]

and

    \[\mathbf{DC}\text{ }=\text{ }\mathbf{3}\text{ }\mathbf{cm},\]

find BC.

Solution:

Given:

Δ ABC and AD bisects ∠A, meeting side BC at D.

    \[~AC\text{ }=\text{ }4.2\text{ }cm\]

,

    \[~DC\text{ }=\text{ }6\text{ }cm,\]

and

    \[BC\text{ }=\text{ }10\text{ }cm.\]

Required to find: AB

Since, AD is the bisector of ∠ A meeting side BC at D in Δ ABC

⇒ AB/ AC = BD/ DC

    \[AB/\text{ }4.2\text{ }=\text{ }BD/\text{ }6\]

We know that,

    \[BD\text{ }=\text{ }BC\text{ }\text{ }DC\text{ }=\text{ }10\text{ }\text{ }6\text{ }=\text{ }4\text{ }cm\]

    \[\Rightarrow AB/\text{ }4.2\text{ }=\text{ }4/\text{ }6\]

    \[AB\text{ }=\text{ }\left( 2\text{ }x\text{ }4.2 \right)/\text{ }3\]

    \[\therefore AB\text{ }=\text{ }2.8\text{ }cm\]

Solution:

Given:

 Δ ABC and AD bisects ∠A, meeting side BC at D.

    \[~AB\text{ }=\text{ }5.6\text{ }cm,\]

    \[AC\text{ }=\text{ }6\text{ }cm,\]

and

    \[DC\text{ }=\text{ }3\text{ }cm.\]

Required to find: BC

AD is the bisector of ∠ A meeting side BC at D in Δ ABC

⇒ AB/ AC = BD/ DC

    \[5.6/\text{ }6\text{ }=\text{ }BD/\text{ }3\]

    \[BD\text{ }=\text{ }5.6/\text{ }2\text{ }=\text{ }2.8cm\]

BD = BC – DC

    \[2.8\text{ }=\text{ }BC\text{ }\text{ }3\]

    \[\therefore BC\text{ }=\text{ }5.8\text{ }cm\]

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