The rectangle shows the outline of a campsite in a national forest. Anna makes a scale drawing of the campsite in which the longer side measures 1 meter. What is the area of the scale drawing in square meters?
If the longer side of the rectangle in the scale drawing measures 1 meter, then the shorter side must also be in proportion to the original campsite's dimensions. Let's say the shorter side in the scale drawing is `x` meters.
This means that the scale factor is `1:x` or `1/x`.
Given that the longer side of the rectangle in the actual campsite is unknown, we'll use `L` meters and `W` meters to represent the length and width of the rectangle in the campsite.
Using the scale factor:
1/x = L/1
L = x
So, the length of the rectangle in the campsite is `x` meters.
Now, the scale factor for the width:
1/x = W/1
W = x
So, the width of the rectangle in the campsite is also `x` meters.
Now, the area of the rectangle in the actual campsite:
Area = L * W
Area = x * x
Area = x^2 square meters
Therefore, the area of the scale drawing is `x^2 square meters`.