(C) In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. According to the Angle Bisector Theorem:$\frac{AB}{AC} = \frac{BD}{D

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(C) In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. According to the Angle Bisector Theorem:$\frac{AB}{AC} = \frac{BD}{DC}$Given $\frac{AB}{5} = \frac{AC}{3}$,we have $\frac{AB}{AC} = \frac{5}{3}$.Substituting the values:$\frac{5}{3} = \frac{4.5}{DC}$$DC = \frac{4.5 \times 3}{5} = 0.9 \times 3 = 2.7$Since $D$ lies on $BC$,$BC = BD + DC$.$BC = 4.5 + 2.7 = 7.2$.

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 $\frac{AB}{5} = \frac{AC}{3}$ and $BD = 4.5$,find $BC$.

A
$4.5$
B
$3.6$
C
$7.2$
D
$6.2$

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $\frac{AB}{5} = \frac{AC}{3}$ and $BD = 4.5$,find $BC$.

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In $\Delta ABC$,$D$ is the midpoint of $\overline{BC}$,$AB = 7$,$AC = 5$ and $AD = 5$. Then $BC = \ldots$

In $\Delta ABC,$ the bisector of $\angle A$ intersects $\overline{BC}$ at $D.$ If $AB = 6,$ $BD = 4$ and $DC = 3,$ find $AC$.

In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

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