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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles3 Marks
Question
In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If $\frac{\text{AD}}{\text{DB}}=\frac{2}{3}$ and AC = 18cm, find AE.
✓

Answer

Given, $\frac{\text{AD}}{\text{DB}}=\frac{2}{3},$ and AC = 18cm
In the figure, DE || BC

$\therefore\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{2}{3}=\frac{\text{AE}}{\text{EC}}$
$\text{Let AE}=\text{x}$
$\therefore\text{EC}=\text{AC}-\text{AE}=18-\text{x}$
$\therefore\frac{\text{x}}{18-\text{x}}=\frac{2}{3}\Rightarrow3\text{x}=36-2\text{x}$
$\Rightarrow3\text{x}+2\text{x}=36\Rightarrow5\text{x}=36$
$\Rightarrow\text{x}=\frac{36}{5}=7.2$
$\therefore\text{AE}=7.2\text{cm}$

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