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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In the figure, if $PB \| CF$ and $DP \| EF, $ then $\frac{\text{AD}}{\text{DE}}=$​​​​​​​
  • A
    $\frac{3}{4}.$
  • ✓
    $\frac{1}{3}.$
  • C
    $\frac{1}{4}.$
  • D
    $\frac{2}{3}.$ 
✓

Answer

Correct option: B.
$\frac{1}{3}.$
In the figure $, PB \| CF, DP \| EF$
$AB = 2\ cm, AC = 8\ cm$
$BC = AC - AB $
$= 8 - 2 = 6\ cm$
In $\triangle\text{ACF},\ \text{BP} \| \text{CF}$
$\therefore\frac{\text{AB}}{\text{BC}}=\frac{\text{AP}}{\text{PF}}=\frac{2}{6}=\frac{1}{3}\ ....(1)$
In $\triangle\text{AEF},\ \text{DP}\|\text{EF}$
$\therefore\frac{\text{AD}}{\text{DE}}=\frac{\text{AP}}{\text{PF}}=\frac{1}{3}\ \ [$From $ (2)]$
$\frac{\text{AD}}{\text{DE}}=\frac{1}{3}.$

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