Question

In ΔABC, ray AD is the bisector of ∠BAC, B-D-C. IF AB = 7.5 cm and AC = 4.5 cm. find BD : DC.​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{In\;\triangle\;ABC,\;AD\;is\;the\;bisector\;of\;\angle{BAC}}$

$\mathsf{AB=7.5\;cm\;\;and\;\;AC=4.5\;cm}$

$\underline{\textbf{To find:}}$

$\textsf{The ratio BD:DC}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Angle bisector theorem:}}$

$\textsf{When a vertical angle of a triangle is bisected, the bisector divides}$

$\textsf{the base into two segments which have same ratio as the order}$

$\textsf{of other two sides}$

$\mathsf{In\;\triangle\;ABC,\;by\;Angle\;bisector\;theorem}$

$\mathsf{\dfrac{BD}{DC}=\dfrac{AB}{AC}}$

$\mathsf{\dfrac{BD}{DC}=\dfrac{7.5}{4.5}}$

$\mathsf{\dfrac{BD}{DC}=\dfrac{75}{45}}$

$\mathsf{\dfrac{BD}{DC}=\dfrac{5}{3}}$

$\implies\boxed{\mathsf{BD:DC=5:3}}$

Answer 2

Given :- In ΔABC, ray AD is the bisector of ∠BAC .If AB = 7.5 cm and AC = 4.5 cm. find BD : DC. ?

Answer :-

given that,

→ AD is angle bisector of ∠BAC .

so,

→ AB/AC = BD/DC { By angle bisector theorem. }

→ 7.5/4.5 = BD/DC

→ 75/45 = BD/DC

→ 5/3 = BD/DC

→ BD : DC = 5 : 3 (Ans.)

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