Ex 13.1, 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
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 13.1, 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
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!