question_answer

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?

Answer:

Let the photograph of bacteria be enlarged x times and length be y cm. As the bacteria enlarged increases, the length also increases in the same ratio. It is a case of direct proportion, i.e., \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}}\]

x (times)	20,000	50,000
Y (cm)	X	5

We have,           \[\frac{20,000}{x}=\frac{50,000}{5}\]

\[\Rightarrow \]               \[x=\frac{20,000\times 5}{50,000}\]

= 2 cm

Thus, enlarged length is 2 cm

and,       actual length of the bacteria

\[=\frac{length}{enl\arg ed\,\,\,time}\]

\[=\frac{5}{50,000}={{10}^{-4}}\]cm