A scale model of a rectangular patio is 6 feet long and 3 feet wide. The actual patio is 15 feet long. What is the area of the actual patio?

112.5

Let x = width

3/6 = x/15

Solve for x and then multiply by length.

To find the area of the actual patio, we need to determine the scale factor between the model and the actual patio. The scale factor is the ratio of the corresponding dimensions in the model and the actual object.

The length of the model patio is 6 feet, and the length of the actual patio is 15 feet. Therefore, the scale factor for the length is 15/6 = 2.5.

Similarly, the width of the model patio is 3 feet, and there is no given width for the actual patio. However, since the length scale factor is 2.5, we can assume the width scale factor is the same. Therefore, the width of the actual patio would be 2.5 times the width of the model patio, which is 3 feet. So, the width of the actual patio is 2.5 * 3 = 7.5 feet.

Now that we have the length and width of the actual patio, we can calculate its area. The area of a rectangle is given by the equation Area = length * width. Therefore, the area of the actual patio is 15 feet * 7.5 feet = 112.5 square feet.

So, the area of the actual patio is 112.5 square feet.

To find the area of the actual patio, we need to use the scale model ratio to scale up the measurements.

The scale model has a length of 6 feet and a width of 3 feet. We know that the actual patio's length is 15 feet. So, we can set up a ratio:

Scale model length : Actual patio length = Scale factor

6 feet : 15 feet = Scale factor

To find the scale factor, we can divide both sides of the ratio by 3:

6 feet ÷ 3 = 15 feet ÷ 3

2 : 5 = Scale factor

So, the scale factor is 2:5.

Now, we can use this scale factor to scale up the width of the scale model. The width of the scale model is 3 feet, so we can multiply it by the scale factor:

3 feet × (2/5) = 6/5 feet = 1.2 feet

Therefore, the actual patio width is 1.2 feet.

To find the area of the actual patio, we multiply the actual length by the actual width:

Actual patio area = 15 feet × 1.2 feet = 18 square feet

So, the area of the actual patio is 18 square feet.