(C) According to the Angle Bisector Theorem,in $\Delta ABC$,if the bisector of $\angle A$ intersects $\overline{BC}$ at $D$,then $\frac{AB}{AC} = \fra

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(C) According to the Angle Bisector Theorem,in $\Delta ABC$,if the bisector of $\angle A$ intersects $\overline{BC}$ at $D$,then $\frac{AB}{AC} = \frac{BD}{DC}$.Given $\frac{AB}{AC} = \frac{3}{4}$ and $BD = 4.5$.Substituting the values: $\frac{3}{4} = \frac{4.5}{DC}$.Therefore,$DC = \frac{4.5 \times 4}{3} = 1.5 \times 4 = 6$.Since $BC = BD + DC$,we have $BC = 4.5 + 6 = 10.5$.

Class 10 Mathematics Triangles Similarity of Triangles and Basic Proportionality Theorem

Medium

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BD = 4.5$,then $BC = \ldots$

A
$4.5$
B
$6$
C
$10.5$
D
$12$

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Similarity of Triangles and Basic Proportionality Theorem

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BD = 4.5$,then $BC = \ldots$

Similar Questions

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 2$,$MB = 5$ and $MN = 4$,find $BC$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AB = 3$ and $AC = 5$,find the length of $BM$.

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.

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