On a map of scale 1:100 000 a rectangular plot of land measures 7cm by 4cm. what are the actual lengths of the plot in kilometers
1 cm = 1 / 100 m
100,000 x 1 cm = 1000 x 1 / 100 = 1,000 m
1,000 m = 1 km
1 cm on scale = 1 km
7 x 4 cm on scale = 7 km x 4 km = 28 km ^ 2
To find the actual lengths of the plot in kilometers, we need to convert the measurements on the map to the corresponding real-world measurements.
Given that the scale is 1:100,000, it means that 1 centimeter on the map represents 100,000 centimeters in real life.
The length of the plot on the map is 7 cm. To find the actual length in kilometers, we need to multiply this by the conversion factor:
Length in real life = Length on the map × Conversion factor
Length in real life = 7 cm × (100,000 cm / 1 cm)
Length in real life = 7 cm × 100,000
Length in real life = 700,000 cm
To convert this to kilometers, we divide by 100,000 (since there are 100,000 centimeters in a kilometer):
Length in kilometers = 700,000 cm ÷ 100,000
Length in kilometers = 7 km
Therefore, the actual length of the plot is 7 kilometers.
To determine the actual lengths of the plot of land, we need to use the concept of scale.
The scale 1:100,000 means that one unit on the map corresponds to 100,000 units in reality. In this case, since the lengths on the map are given in centimeters, we need to convert the measurements to kilometers.
First, let's convert the length in centimeters to kilometers. Since there are 100,000 centimeters in a kilometer, we divide the length in centimeters by 100,000 to get the length in kilometers.
Length in kilometers = Length in centimeters / 100,000
For the given rectangular plot of land, the length is 7 centimeters. Let's plug in the values into the formula:
Length in kilometers = 7 cm / 100,000
Calculating this, we find:
Length in kilometers = 0.00007 kilometers
Similarly, let's calculate the width:
Width in kilometers = 4 cm / 100,000
Width in kilometers = 0.00004 kilometers
Therefore, the actual lengths of the plot of land are 0.00007 kilometers by 0.00004 kilometers.