An architect makes a model of a new house with a patio made with pavers. in the model, each paver in the patio is 1/3 in. long and 1/6 wide. the actual dimensions of pavers are shown: 1/8 ft and 1/4ft. what is the constant of proportionality that relates the length of a paver in the model and the length of an actual paver? what is the constant of proportionality that relates the area of an actual paver?

The constant of proportionality between the actual dimensions of the pavers and the model is 9.

The proportionality constant for the area is 81.

Step-by-step explanation:

To solve this problem, let's transform all quantities to the same units (inches)

The actual dimensions of the pavers are:

Then we divide the real dimensions between those of the model:

Width:

Long =

Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.

Actual length = model length * (9)

The "A" area of a paver is the product of its width multiplied by its length.

So:

(real width) * (real length) = ((9) Model width) * ((9) model length)

(real width) * (real length) = * (Model width) * (model length)

(real area) = 81 * (Model area)

The proportionality constant for the area is 81.

The length of a paver in the model and the length is 1/9.

The constant of proportionality that relates the area 1/81.

Step-by-step explanation:

Area of rectangle is

Dimensions of paver in model:

Area of model

The area of the model is 1/18 square inches.

We know that 1 ft = 12 inches

Actual dimensions of paver:

Actual area is

The actual area is 4.5 square inches.

The constant of proportionality that relates the length of a paver in the model and the length of an actual paver is

The length of a paver in the model and the length is 1/9.

The constant of proportionality that relates the area of an actual paver is

The constant of proportionality that relates the area 1/81.