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, find the corresponding median of the other.

Answer 1

SOLUTION :  

Given : Area of two similar triangles is 121cm² and 64 cm² .

Since, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians.

ar(∆1)/ar(∆2) = (median1/median2)²

121 / 64 = (12.1/median2)²

On taking square root on both sides,

√121 / 64 = √(12.1/median2)²

11/8 = 12.1 /median2

11× Median2 = 12.1 × 8

Median 2 = (12.1× 8)/11

Median2 = 1.1 × 8

Median2  = 8.8 cm

Hence, the corresponding median of the other is 8.8 cm.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hello user


Since , we know that the medians of two similar triangles are proportional to the square root of the ratio of their areas

So,

Let the median of other triangle be x

(121/64)^1/2 = 12.1/x

11/8 = 12.1/x

x = 8 × 12.1 / 11

x = 1.1 × 8

x = 8.8 cm

So, the median of other triangle will be 8.8 cm.


Hope it works