Question

The areas of two similar triangles are $121$ cm${}^2$ and $64$ cm${}^2$, respectively. If the median of the first triangle is $12.1$ cm, then the corresponding median of the other is:

• A. $6.4$ cm
• B. $10$ cm
• C. $8.8$ cm
• D. $3.2$ cm

Answer 1

Answer: (C)

$8.8$ cm

The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding medians. Therefore,
$\frac{121}{64}=\frac{{\left(12.1\right)}^2}{x^2},$ where $x$ is the median of the other $△.$
$\Rightarrow$ $x^2=\frac{{\left(12.1\right)}^2\times 64}{121}\Rightarrow x=\sqrt{\frac{121}{100}\times 64}$
$=\frac{11}{10}\times 8=8.8$ cm.