Question

The areas of two similar triangles are 100 $c{m}^2$ and 64 $c{m}^2$ respectively. If the median of greater side of the first triangle is 13 cm, find the corresponding median of the other triangle.

• A. 20 cm
• B. 15 cm
• C. 10 cm
• D. 10.4 cm

Answer 1

The correct option is D 10.4 cm

Given that the areas of two similar triangles are $100c{m}^2$ and $64c{m}^2$.

and median of greater triangle is $13cm$.

Let the median of the other triangle be $xcm$

We know that, the areas of two similar triangles are in the ratio of the squares of their corresponding sides or medians.

The ratio of the areas of triangles $=\frac{100}{64}=\frac{25}{16}$

$\therefore \frac{(13{)}^2}{(x{)}^2}=\frac{25}{16}$

$\Rightarrow \frac{169}{x^2}=\frac{25}{16}$

$\Rightarrow 25x^2=169\times 16$

$\Rightarrow x^2=\frac{2704}{25}=108.16$

$\Rightarrow x=10.4cm$

Hence, the median of the other triangle is $10.4cm$