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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
It is given that $\triangle\text{ABC}\sim\triangle\text{DFE}.$ If $\angle\text{A}=30^\circ,\angle\text{C}=50^\circ,\text{AB}=5\text{cm},\text{AC}=8\text{cm}$ and $\text{DF}=7.5\text{cm}$ then which of the following is true?
  • A
    $\text{DE}=12\text{cm},\angle\text{F}=50^\circ$
  • ✓
    $\text{DE}=12\text{cm},\angle\text{F}=100^\circ$
  • C
    $\text{EF}=12\text{cm},\angle\text{D}=100^\circ$
  • D
    $\text{EF}=12\text{cm},\angle\text{D}=30^\circ$
✓

Answer

Correct option: B.
$\text{DE}=12\text{cm},\angle\text{F}=100^\circ$
Given that,
$\angle\text{A}=30^\circ,\angle\text{C}=50^\circ$
$\triangle\text{ABC}\sim\triangle\text{DFE}$
$\Rightarrow\angle\text{A}=\angle\text{D}=30^\circ$
$\angle\text{C}=\angle\text{E}=50^\circ$
Using angle sum property, we can find $\angle\text{B}=100^\circ$
So, $\angle\text{B}=\angle\text{F}=100^\circ$
Also, AB = 5cm, AC = 8cm and DF = 7.5cm
$\frac{\text{AB}}{\text{DF}}=\frac{\text{BC}}{\text{FE}}=\frac{\text{AC}}{\text{DE}}$
$\Rightarrow\frac{5}{7.5}=\frac{\text{BC}}{\text{FE}}=\frac{8}{\text{DE}}$
$\Rightarrow\frac{5}{7.5}=\frac{8}{\text{DE}}\Rightarrow\frac{8\times7.5}{5}=12\text{cm}$
Hence, DE = 12cm and $\angle\text{F}=100^\circ$

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