Ex 11.1, 9 - Chapter 11 Class 8 Direct and Inverse Proportions

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 11.1, 9 A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high
Let’s first convert all lengths in cm
5 m 60 cm
= 5 m + 60 cm
= 5 × 100 cm + 60 cm
= 500 + 60
= 560 cm
3 m 20 cm
= 3 m + 20 cm
= 3 × 100 cm + 20 cm
= 300 + 20
= 320 cm
10 m 50 cm
= 10 m + 50 cm
= 10 × 100 cm + 50 cm
= 1000 + 50
= 1050 cm
Ex 11.1, 9 A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high
Let’s first convert all lengths in cm
5 m 60 cm
= 5 m + 60 cm
= 5 × 100 cm + 60 cm
= 500 + 60
= 560 cm
3 m 20 cm = 3 m + 20 cm
= 3 × 100 cm + 20 cm
= 300 + 20 = 320 cm
10 m 50 cm = 10 m + 50 cm
So, our question becomes
A 560 cm high vertical pole casts a shadow 320 cm long
We need to find length of shadow cast by pole of height 1050 cm
Let y cm be the length of shadow cast by pole of height 1050 cm
Thus, our table looks like
Now, as height of pole increases,
Length of shadow also increases
∴ They are in direct proportion
𝟓𝟔𝟎/𝟑𝟐𝟎 = 𝟏𝟎𝟓𝟎/𝒚
56/32 = 1050/𝑦
56 × 𝑦 = 1050 × 32
𝒚 = (𝟏𝟎𝟓𝟎 × 𝟑𝟐)/𝟓𝟔
𝑦 = (1050 × 16)/28
𝑦 = (1050 × 4)/7
𝑦 = 150 × 4
𝒚 = 𝟔𝟎𝟎 cm
𝑦 = 6 m
∴ Length of shadow is 6 m
Ex 11.1, 9 A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (ii) the height of a pole which casts a shadow 5m long.Now,
We need to find height of pole casting a shadow of 5 m i.e. 500 cm
Let x be the height of pole which casts a shadow of 500 cm
Thus, our table looks like
Now, height of pole and Length of shadow are in direct proportion
𝟓𝟔𝟎/𝟑𝟐𝟎 = 𝒙/𝟓𝟎𝟎
56/32 = 𝑥/500
56 × 500 = 𝑥 × 32
28000 = 32x
28000/32 = 𝑥
𝑥 = 28000/32
𝒙 = 875 cm
𝑥 = 8 m 75 cm
∴ Height of the pole is 8 m 75 cm

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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