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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In $\triangle\text{ABC}$ and $\triangle\text{DEF},$ we have $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{5}{7},$ then $\text{ar}(\triangle\text{ABC}):\text{ar}(\triangle\text{DEF})=?$
  • A
    5 : 7
  • ✓
    25 : 49
  • C
    49 : 25
  • D
    125 : 343
✓

Answer

Correct option: B.
25 : 49
In $\triangle\text{ABC}$ and $\triangle\text{DEF},$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DF}}=\frac{5}{7}$
$\Rightarrow\triangle\text{ABC}\sim\triangle\text{DEF}$ ....(SSS criterion for Similarity)
$\Rightarrow\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{DEF})}=\frac{\text{AB}^2}{\text{DE}^2}=\frac{5^2}{7^2}=\frac{25}{49}$
So, the ratio is 25 : 49.

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