Answer & Solution
Answer: Option
A
Solution:
Understanding the Problem:
We have a rectangular plot of land in real life that is 200 meters long and 400 meters wide.
This plot is drawn on a sheet of paper as a smaller rectangle.
The area of the rectangle on the paper is 800 square millimeters (mm²).
We need to find the scale of the drawing, which tells us how many meters are represented by each millimeter on the paper.
Finding the Scale:
First, let's find the area of the real-life plot:
Area = length × width = 200m × 400m = 80,000 m²
Now, let's compare the area on the paper to the real-life area:
The paper area is 800 mm², and the real area is 80,000 m².
To find the scale, we need to figure out how many square meters are represented by one square millimeter on the paper.
We can do this by dividing the real area by the paper area:
80,000 m² / 800 mm² = 100 m²/mm²
This means that 1 mm² on the paper represents 100 m² in real life.
To find the linear scale (how many meters per millimeter), we need to take the square root of this value:
√100 m²/mm² = 10 m/mm
Therefore, the scale of the drawing is 1 mm = 10 m
Correct Option:
The correct answer is Option A: 1mm = 10m
