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.

This video is only available for Teachoo black users

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)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.