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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
The areas of two similar triangles $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are $144cm^2$ and $81cm^2$ respectively. If the longest side of larger $\triangle\text{ABC}$ be $36\ cm$, then the longest side of the smaller triangle $\triangle\text{DEF}$ is:
  • A
    $20\ cm.$
  • B
    $26\ cm.$
  • ✓
    $27\ cm.$
  • D
    $30\ cm.$
✓

Answer

Correct option: C.
$27\ cm.$
Given: Areas of two similar triangles $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are $114\ cm^2$ and $81cm^2.$
If the longest side of larger $\triangle\text{ABC}$ is 36cm
To find: the longest side of the smaller triangle $\triangle\text{DEF}$
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{DEF})}=\Big(\frac{\text{longest side of larger }\triangle\text{ABC}}{\text{longest side of smaller }\triangle\text{DEF}}\Big)^2$
$\frac{144}{81}=\Big(\frac{36}{\text{longest side of smaller}\ \triangle\text{DEF}}\Big)^2$
Taking aquare root on both sides, we get
$\frac{12}{9}=\frac{36}{\text{longest side of smaller}\ \triangle\text{DEF}}$
longest side of smaller $\triangle\text{DEF}=\frac{36\times9}{12}=27\text{cm}$
Hence the correct answer is $C.$

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