Question

Use the scale factor to compare the perimeter and area of the original figure of the enlarged figure. Complete the statements about the relationship
between the two figures.
The scale factor is
The perimeter of the enlarged rectangle can be found
by multiplying the scale factor and the original
perimeter to get
7 times the area of the
The area of the scale model is
original figure.​

Answer 1

Answer:

Part 1) The scale factor is 2

Part 2) The perimeter of the enlarged rectangle is 19 units

Part 3) The area of the enlarged rectangle is 19.5 square units (the area of the enlarged rectangle is 4 times the area of the original rectangle)

Step-by-step explanation:

we know that

A dilation is a non-rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The ratio of its perimeter is equal to the scale factor and the ratio of its areas is equal to the scale factor squared

step 1

Find the scale factor

Let

z ---> the scale factor

$z=\frac{3}{1.5}=2$

step 2

Find the perimeter of the enlarged rectangle

Multiply the perimeter of the original rectangle by the scale factor

The perimeter of the original rectangle is

$P=2(1.5+3.25)=9.5\ units$

so

The perimeter of the enlarged rectangle is

$9.5(2)=19\ units$

step 3

Find the area of the enlarged rectangle

Multiply the area of the original rectangle by the scale factor squared

The area of the original rectangle is

$A=(1.5)(3.25)=4.875\ units^2$

so

The area of the enlarged rectangle is

$4.875(2^2)=19.5\ units^2$

The area of the enlarged rectangle is 4 times the area of the original rectangle

step 4

Find the value of b

Multiply the corresponding side of the original rectangle by the scale factor

$b=3.25(2)=6.50\ units$

Verify the perimeter of the enlarged rectangle

$P=2(3+6.50)=19\ units$ ----> is ok

Verify the area of the enlarged rectangle

$A=3(6.50)=19.5\ units^2$ ---> is ok

Answer 2

Answer:

Part 1: The scale factor is 2.

Part 2: The perimeter of the enlarged rectangle can be found by multiplying the scale factor and the original perimeter to get 19.

Part 3: The area of the scale model is 4 times the area of the original figure.

Step-by-step explanation:

I know because i just did the quiz.