Given : Sujal makes the sail of his model in the shape of a triangle with sides 5cm, 4 cm and 6 cm   for actual size of 10 m , 8 m and 12 m  

pole in the actual boat is of length 9m

To Find : Which criteria of similarity  used

 what will be the length of the pole in  the model?

Solution:

criteria of similarity  used is SSS   ( Side - Side - Side )

10 m / 5 cm = 9 m / x cm

=> x = 4.5 cm

length of the pole in  the model = 4.5 cm

Ratio  5 cm  : 10 m

5 cm = 1000 cm

1 : 200

Ratio of corresponding median is same as ratio of corresponding sides for similar triangles

Corresponding medians of these triangles are in the ratio = 1 : 200

if square of one side is equal to the sum of the squares of the other two

sides, then the angle opposite the first side is a right angle This theorem is called as  Converse of Pythagoras theorem

ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides

ratio of areas of the triangular sail of the  model and of the actual boat

= 1² : 200²

= 1 : 40000

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