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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In a $\triangle\text{ABC},$ if $DE$ is drawn parallel to $BC,$ cutting $AB$ and $AC$ at $D$ and $E$ respectively such that $AB = 7.2\ cm, AC = 6.4\ cm$ and $AD = 4.5\ cm$. Then $, AE =?$
  • A
    $5.4\ cm$
  • ✓
    $4\ cm$
  • C
    $3.6\ cm$
  • D
    $3.2\ cm$
✓

Answer

Correct option: B.
$4\ cm$
In $\triangle\text{ABC},\text{DE }\|\text{ BC}$
By Basic proportionality theorem,
$\frac{\text{AE}}{\text{AC}}=\frac{\text{AD}}{\text{AB}}$
$\Rightarrow\frac{\text{AE}}{6.4}=\frac{4.5}{7.2}$
$\Rightarrow\text{AE}=\frac{4.5\times6.4}{7.2}$
$\Rightarrow\text{AE}=4\text{ cm}$

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