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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
It is given that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and $\frac{\text{BC}}{\text{QR}}=\frac{2}{3}$ then $\frac{\text{ar}(\triangle\text{PQR})}{\text{ar}(\triangle\text{ABC})}=?$
  • A
    $\frac{2}{3}$
  • B
    $\frac{3}{2}$
  • C
    $\frac{4}{9}$
  • ✓
    $\frac{9}{4}$
✓

Answer

Correct option: D.
$\frac{9}{4}$
$\triangle\text{ABC}\sim\triangle\text{PQR}$ and $\frac{\text{BC}}{\text{QR}}=\frac{2}{3}$
$\Rightarrow\frac{\text{QR}}{\text{BC}}=\frac{3}{2}$
$\frac{\text{ar}(\triangle\text{PQR})}{\text{ar}(\triangle\text{ABC})}=\frac{\text{QR}^2}{\text{BC}^2}$
$=\frac{3^2}{2^2}=\frac{9}{4}$
So, the ratio is $9 : 4.$

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