Question

The areas of two similar triangles $△ABC$ and $△DEF$ are $144c{m}^2$ and $81c{m}^2$ respectively. If the longest side of larger $△ABC$ be $36cm$, then, the largest side of the similar triangle $△DEF$ is

• A. $20cm$
• B. $26cm$
• C. $27cm$
• D. $30cm$

Answer 1

The correct option is C $27cm$

Ratio of areas of similar triangle $=(sides{)}^2$

$\frac{ar\Delta ABC}{ar\Delta DEF}=\frac{144}{81}$

Let the Largest of the triangle $DEF=x$

$(\frac{36}{x}{)}^2=\frac{144}{81}$

$\Rightarrow \frac{36}{x}=\sqrt{\frac{144}{81}}$

$\Rightarrow \frac{36}{x}=\frac{12}{9}$

$\Rightarrow x=\frac{36\times 9}{12}\Rightarrow x=27cm$

Option C