Question 1 - Case Based Questions (MCQ) - Chapter 6 Class 10 Triangles
Last updated at April 16, 2024 by Teachoo
Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the
ground.
Question 1
What is the height of the tower?
(a) 20 m
(b) 50 m
(c) 100 m
(d) 200 m
Question 2
What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?
(a) 75 m
(b) 50 m
(c) 45 m
(d) 60 m
Question 3
What is the height of Ajay’s house?
(a) 30 m
(b) 40 m
(c) 50 m
(d) 20m
Question 4
When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?
(a) 16 m
(b) 32 m
(c) 20 m
(d) 8 m
Question 5
When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house?
(a) 15 m
(b) 32 m
(c) 16 m
(d) 8 m
Transcript
Question Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijayβs house if 20m when Vijayβs house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.
Question 1 What is the height of the tower? (a) 20 m (b) 50 m (c) 100 m (d) 200 m
Since the triangles are similar
Their sides are proportional
(π―πππππ ππ π½ππππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π½ππππ^β² π πππππ)=(π―πππππ ππ π»ππππ)/(π³πππππ ππ ππππ ππ ππ π»ππππ)
20/10=(π»πππβπ‘ ππ πππ€ππ)/50
50 Γ 2 = Height of Tower
Height of Tower = 100 m
So, the correct answer is (c)
Question 2 What will be the length of the shadow of the tower when Vijayβs house casts a shadow of 12 m? (a) 75 m (b) 50 m (c) 45 m (d) 60 m
If Vijayβs house casts a shadow of 12 m,
Then
(π―πππππ ππ π½ππππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π½ππππ^β² π πππππ)=(π―πππππ ππ π»ππππ)/(π³πππππ ππ ππππ ππ ππ π»ππππ)
20/12=100/(πΏππππ‘β ππ π βππππ€ ππ πππ€ππ)
Length of shadow of tower = 100 Γ 12/20
Length of shadow of tower = 5 Γ 12
Length of shadow of tower = 60 m
So, the correct answer is (d)
Question 3 What is the height of Ajayβs house? (a) 30 m (b) 40 m (c) 50 m (d) 20m
Since the triangles are similar
Their sides are proportional
(π―πππππ ππ π½ππππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π½ππππ^β² π πππππ)=(π―πππππ ππ π¨πππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π¨πππ^β² π πππππ)
20/10=(π―πππππ ππ π¨πππ^β² π πππππ)/20
20 Γ 2 = Height of Ajayβs house
Height of Ajayβs house = 40 m
So, the correct answer is (b)
Question 4 When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajayβs house? (a) 16 m (b) 32 m (c) 20 m (d) 8 m
Since the triangles are similar
Their sides are proportional
(π―πππππ ππ π»ππππ)/(π³πππππ ππ ππππ ππ ππ π»ππππ)=(π―πππππ ππ π¨πππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π¨πππ^β² π πππππ)
100/40=ππ/(π³πππππ ππ ππππ ππ ππ π¨πππ^β² π πππππ)
Length of shadow of Ajayβs house = 40 Γ 40/100
Length of shadow of Ajayβs house = 4 Γ 4
Length of shadow of Ajayβs house = 16 m
So, the correct answer is (a)
Question 5 When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijayβs house? (a) 15 m (b) 32 m (c) 16 m (d) 8 m
Since the triangles are similar
Their sides are proportional
(π―πππππ ππ π»ππππ)/(π³πππππ ππ ππππ ππ ππ π»ππππ)=(π―πππππ ππ π½ππππ^β² π πππππ)/(π³πππππ ππ ππππ ππ ππ π½ππππ^β² π πππππ)
100/40=ππ/(π³πππππ ππ ππππ ππ ππ π½ππππ^β² π πππππ)
Length of shadow of Vijayβs house = 20 Γ 40/100
Length of shadow of Vijayβs house = 2 Γ 4
Length of shadow of Vijayβs house = 8 m
So, the correct answer is (d)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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