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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In the adjoining figure$\text{ AC}\parallel\text{BD.AC}\parallel\text{BD}$. If $, EB = 4\ cm, ED = 8\ cm, AC = 6\ cm, AE = 3\ cm$ then $CE$ and $BD$ are respectively :​​​​​​​
  • A
    $7.5\ cm, 9.5\ cm.$
  • ✓
    $6\ cm, 8\ cm.$
  • C
    $4\ cm, 6\ cm.$
  • D
    $5\ cm, 7\ cm.$
✓

Answer

Correct option: B.
$6\ cm, 8\ cm.$
Given : $\frac{\text{AC}}{\text{BD}}.$ and $AC = 6\ cm, AE = 3\ cm, EB = 4\ cm, ED = 8\ cm.$
In $\triangle\text{ACE}$ and $\text{DEB}, \angle\text{AEC}=\angle\text{DEB} \ [$vertically opposite angles$]$
$\angle\text{ECA}=\angle\text{EDB}$ Alternet angles as $\text{AC}\parallel\text{BD}$
$\therefore\triangle\text{ACE}\sim\triangle\text{DEB}\ [\text{AA}$ similarity$]$
$\therefore\frac{\text{EB}}{\text{AE}}=\frac{\text{ED}}{\text{EC}}$
$\Rightarrow\frac{4}{3}=\frac{8}{\text{EC}}$
$\Rightarrow\text{EC}=\frac{8\times3}{4}=6\text{ cm}$
Also $\frac{\text{EB}}{\text{AE}}=\frac{\text{BD}}{\text{AC}}$
$\Rightarrow\frac{4}{3}=\frac{\text{BD}}{6}$
$\Rightarrow\text{BD}=\frac{4\times6}{3}=8\text{ cm}$

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