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Answer :
Given that the area of the plan of an old survey plotted to a scale of 10 meters to 1 cm measures now as 100.2 sq. cm as found by a planimeter.
The plan is found to have shrunk so that a line originally 10 cm long now measures 9.7 cm only.
We need to find the shrunk scale and the true area of the survey.
Let the true length of the line be x.
The scale of the plan is 10 m = 1 cm, so, 1 m = 1/100 cm.
The area of the plan of the old survey is 10 × 100 × 100 = 100000 cm².
The old length of the line, l = 10/1 cm = 100 cm
The new length of the line, l1 = 9.7/1 cm = 97 cm
So,
the shrunk scale, S = l1/l= 97/100
Let A be the true area of the survey.
Then, A = 100.2/ S² sq. cm (formula of the shrunk area)
Putting the value of S, we get:
A = 100.2/(97/100)²= 106.7114 sq. cm
The shrunk scale is 97/100 and the true area of the survey is 106.7114 sq. cm.
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