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

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 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)