Question

The area of two similar triangles are in ratio 7 : 11 find the ratio of their corresponding medians​

Answer 1

Answer:

According to theorem,

The ratio of two similar triangles are equal to ratios of squares of the corresponding sides and medians.

$\frac{area(1)}{area(2)} = \frac{ {(median1)}^{2} }{ {(median2)}^{2} }$

$\frac{7}{11} = \frac{ {x}^{2} }{ {y}^{2} }$

$\frac{x}{y} = \frac{ \sqrt{7} }{ \sqrt{11} }$

Answer 2

Given:

The area of two similar triangles are in ratio 7 : 11

To find:

the ratio of their corresponding medians​

Solution:

As per the rule of the similarity, the ratio of the area of the similar triangles must be equal to the square of the ratio of the sides of the respective triangles.

Which can be represented as:

$\frac{Area~of~T_{1}}{Area ~of ~T_{2}} = (\frac{side ~of~ T_{1}}{side ~of ~ T_{2}})^{2}$

as we also know that:

$\frac{side ~of~ T_{1}}{side ~of ~ T_{2}} = \frac{Median ~of~ T_{1}}{Median ~of ~ T_{2}}$

So we get the term as:

$\frac{Area ~of~ T_{1}}{Area ~of ~ T_{2}}= (\frac{Median ~of~ T_{1}}{Median ~of ~ T_{2}})^{2}$

we have given the ratio as:

$\frac{Area ~of~ T_{1}}{Area ~of ~ T_{2}}= \frac{7}{11}$

we get:

$\frac{7}{11} = (\frac{Median ~of~ T_{1}}{Median ~of ~ T_{2}})^{2}$

$\frac{Median ~of~ T_{1}}{Median ~of ~ T_{2}} = \sqrt{\frac{7}{11} }$

Hence,

The ratio of their corresponding medians​ is $\sqrt{\frac{7}{11} }$