Question

The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, then the corresponding median of the other triangle is

Options

• 11 cm

•  8.8 cm

• 11.1 cm

• 8.1 cm

Answer 1

Given: The area of two similar triangles is 121cm² and 64cm² respectively. The median of the first triangle is 2.1cm.

To find: Corresponding medians of the other triangle

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their medians.

`\text{ar(triangle 1)}/\text{ar(triangle 1)}=((\text{median} 1^2)/(\text{median2}^2))^2`

`121/64=((12.1)/\text{median2})^2`

Taking square root on both side, we get

\[\frac{11}{8} = \frac{12 . 1cm}{median2}\]
\[ \Rightarrow median2 = 8 . 8 cm\]

Hence the correct answer is `b`.