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Triangles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $AB = 9.1cm$ and $DE = 6.5cm$. If the perimeter of $\triangle\text{DEF}$ is 25cm, then the perimeter of $\triangle\text{ABC}$ is:
  • A
    $36cm.$
  • B
    $30cm.$
  • C
    $34cm.$
  • ✓
    $35cm.$
✓

Answer

Correct option: D.
$35cm.$
Given: $\triangle\text{ABC}$ is similar to $\triangle\text{DEF}$ such that $AB= 9.1cm, DE = 6.5cm$. Perimeter of $\triangle\text{DEF}$ is $25cm$.
To find: Perimeter of $\triangle\text{ABC}.$
We know that the ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters.
Hence,
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{AC}}{\text{DE}}=\frac{\text{P1}}{\text{P2}}$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{P}(\triangle\text{ABC})}{\text{P}(\triangle\text{DEF})}$
$\frac{9.1}{6.5}=\frac{\text{P}(\triangle\text{ABC})}{25}$
$\text{P}(\triangle\text{ABC})=\frac{9.1\times25}{6.5}$
$\text{P}(\triangle\text{ABC})=35\text{cm}$
Hence the correct answer is $D$.

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