Ex 13.1, 5 A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Given,
Length of bacteria is 5 cm if its photograph is enlarged 50,000 times
Finding the actual length of bacteria
Let the actual length of bacteria = x cm
Since bacteria is englarged 50,000 times to 5 cm
50,000 × Actual Length = 5 cm
50,000 × 𝑥 = 5
𝑥 = 5/50,000 cm
𝑥 = 1/10,000 cm
𝑥 = 1/(〖10〗^4 ) cm
𝑥 = 1×〖10〗^(−4) cm
∴ Actual length of bacteria is 𝟏×〖𝟏𝟎〗^(−𝟒) cm
Now, our question is
If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Finding the enlarged length
Now, given that
Length of bacteria is 5 cm if its photograph is enlarged 50,000 times
Let y cm be the length of bacteria if the photograph is enlarged 20,000 times
Thus, our table looks like
As photograph is enlarged,
The length of bacteria also increases,
∴ Length and enlarged photograph are in direct proportion.
50,000/5 = 20,000/𝑦
10,000 = 20,000/𝑦
10,000 = 20,000/𝑦
10,000×𝑦 = 20,000
𝑦 = 20,000/10,000
𝑦 = 2 cm
∴ The enlarged length of bacteria = 2 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.

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