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? 3 width 4 height

Question

Create a visually pleasing, text-free image that portrays a rectangular National Forest campsite with lush green vegetation and towering trees surrounding it. The campsite's perimeter consists of a clear outline with the longer side measuring approximately one meter. Make sure to apply the right scale, presenting a broad, continuous view of the enclosure. The ratio of the dimensions of the rectangle should reflect a 3:4 aspect ratio, with the width being 3 and the taller side being 4. No people or animals should be in the enclosure - the focus is entirely on the landscape and the rectangle outline.

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? 3 width 4 height

Answer 1

To find the area of the scale drawing in square meters, we need to first determine the dimensions of the scale drawing.

Given that the longer side of the rectangle in the campsite measures 1 meter, we can assume that this measurement corresponds to the longer side of the scale drawing.

Since we have the width (3 meters) and height (4 meters) of the original campsite, we can create proportions to find the corresponding dimensions of the scale drawing.

Original Campsite:
Width = 3 meters
Height = 4 meters

Scale Drawing:
Width = x meters
Height = y meters

Proportion: Width of Original Campsite / Width of Scale Drawing = Height of Original Campsite / Height of Scale Drawing

3 meters / x meters = 4 meters / y meters

We can rewrite this proportion as:

3 / x = 4 / y

Now, we can solve for y:

Cross multiplying, we get:
4x = 3y

Dividing by 3, we get:
y = (4x) / 3

Since we know that the longer side of the scale drawing is 1 meter, we can substitute x = 1 in the equation above:

y = (4 * 1) / 3
y = 4 / 3
y = 1.33 meters

So, the scale drawing has a width of 1 meter and a height of 1.33 meters.

To find the area of the scale drawing, we multiply the width and height:

Area of Scale Drawing = Width * Height
Area of Scale Drawing = 1 meter * 1.33 meters
Area of Scale Drawing = 1.33 square meters

Therefore, the area of the scale drawing is 1.33 square meters.

Answer 2

If the longer side of the campsite measures 1 meter, then the shorter side must measure 3/4 of a meter (since the rectangle has a width-to-length ratio of 3:4).

To find the area of the scale drawing, we need to multiply the dimensions of the rectangle in the scale drawing. The dimensions of the shorter side and longer side in the scale drawing are 3/4 meter and 1 meter, respectively.

So the area of the scale drawing is:

(3/4) meter x 1 meter = 3/4 square meters

Therefore, the area of the scale drawing of the campsite is 3/4 square meters.

Answer 3

To find the area of the scale drawing, we need to multiply the length of one side by the length of the other side.

In this case, the longer side measures 1 meter. The shorter side is not given, so we need to determine it based on the given width and height.

Given that the width is 3 and the height is 4, we can assume that the shorter side corresponds to the width in the scale drawing.

To find the length of the shorter side in the scale drawing, we can set up the following proportion:

Length of shorter side in scale drawing / Length of longer side in scale drawing = Width of campsite / Length of longer side of campsite

Let's plug in the values:

x / 1 = 3 / 1

Cross multiplying, we have:

x = 3

So, the length of the shorter side in the scale drawing is 3 meters.

Now, we can find the area by multiplying the length and width of the scale drawing:

Area = 3 meters x 1 meter = 3 square meters.

Therefore, the area of the scale drawing is 3 square meters.