(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 Mix Examples - Triangles

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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 $BC = \ldots$

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

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In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude. If $PD = 9 DR$,then $PQ = \ldots \ldots \ldots \times QR$.

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In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XP:PY = 3:5$ and $XZ = 5.6$,find $QZ$.

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In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is a median. If $m \angle C = 30^{\circ}$ and $AB = 5$,find $BD$.

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In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

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In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 8$,$MB = 12$ and $MC = 6$,find $MD$.

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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 $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude. If $PD = 9 DR$,then $PQ = \ldots \ldots \ldots \times QR$.

In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XP:PY = 3:5$ and $XZ = 5.6$,find $QZ$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is a median. If $m \angle C = 30^{\circ}$ and $AB = 5$,find $BD$.

In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 8$,$MB = 12$ and $MC = 6$,find $MD$.

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