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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 $\frac{\text{AD}}{\text{BD}}=\frac{4}{5}$ and EC = 2.5cm, find AE.
✓

Answer

Given: $\frac{\text{AD}}{\text{BD}}=\frac{4}{5}$ and EC = 2.5cm
by thales theorem,
$\frac{\text{AD}}{\text{BD}}=\frac{\text{AE}}{\text{CE}}$
$\Rightarrow\frac{4}{5}=\frac{\text{AE}}{2.5}\ \ (\because\text{CE}=\text{EC})$
$\Rightarrow\text{AE}=\frac{4\times2.5}{5}$
$\Rightarrow\text{AE}=2\text{cm}$

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