Sujal makes the sail of his model in the shape of a triangle with sides 5cm, 4 cm and
6 cm. Which criteria of similarity did Sujal use?
a) AAA b) SAS c) SSS d) RHS(ii) If the pole in the actual boat is of length 9m, what will be the length of the pole in
the model?
a) 9 cm b) 6 cm c) 4.5 cm d) 3 cm(iii) Sides of two similar triangles of the model and the actual sail are in the ratio 1:200.
Corresponding medians of these triangles are in the ratio,
a) 1:40000 b) 1:20000 c) 1: 200 d) 1:100(iv) In a triangle, 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,
a) Pythagoras theorem b) Thales theorem
c) Converse of Thales theorem d) Converse of Pythagoras theorem(v) If ratio of the areas of two similar triangles is equal to the square of the ratio of
their corresponding sides then , What is the ratio of areas of the triangular sail of the
model and of the actual boat ?
a) 1:40000 b) 1:20000 c) 1: 200 d) 1:100
Answers
Answer:
(i) c
(ii) c
(iii) b
(iv) a
(v) c
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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