Question 1 - Case Based Questions (MCQ) - Chapter 6 Class 10 Triangles (Term 1)

Last updated at Aug. 17, 2021 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

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 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
Since the triangles are similar
Their sides are proportional
(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)
20/10=(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑇𝑜𝑤𝑒𝑟)/50
50 × 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 Vijay’s house casts a shadow of 12 m? (a) 75 m (b) 50 m (c) 45 m (d) 60 m
If Vijay’s house casts a shadow of 12 m,
Then
(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)
20/12=100/(𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠ℎ𝑎𝑑𝑜𝑤 𝑜𝑓 𝑇𝑜𝑤𝑒𝑟)
Length of shadow of tower = 100 × 12/20
Length of shadow of tower = 5 × 12
Length of shadow of tower = 60 m
So, the correct answer is (d)
Question 3 What is the height of Ajay’s house? (a) 30 m (b) 40 m (c) 50 m (d) 20m
Since the triangles are similar
Their sides are proportional
(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)
20/10=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/20
20 × 2 = Height of Ajay’s house
Height of Ajay’s 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 Ajay’s house? (a) 16 m (b) 32 m (c) 20 m (d) 8 m
Since the triangles are similar
Their sides are proportional
(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)
100/40=𝟒𝟎/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑨𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)
Length of shadow of Ajay’s house = 40 × 40/100
Length of shadow of Ajay’s house = 4 × 4
Length of shadow of Ajay’s 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 Vijay’s house? (a) 15 m (b) 32 m (c) 16 m (d) 8 m
Since the triangles are similar
Their sides are proportional
(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑻𝒐𝒘𝒆𝒓)=(𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)
100/40=𝟐𝟎/(𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒔𝒉𝒂𝒅𝒐𝒘 𝒐𝒇 𝑽𝒊𝒋𝒂𝒚^′ 𝒔 𝒉𝒐𝒖𝒔𝒆)
Length of shadow of Vijay’s house = 20 × 40/100
Length of shadow of Vijay’s house = 2 × 4
Length of shadow of Vijay’s house = 8 m
So, the correct answer is (d)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.