Question

What is the perimeter of the larger of the two similar parallelograms?





10.5 cm

14 cm

18 cm

21 cm
(Gotta attach file)

Answer 1

What do you know about the lengths of the opposite sides of a parallelogram?

Answer 2

I know you take the CM and multiply them both by 2 and then add them.

Answer 3

You need a perimeter. That means you need to add the lengths of all 4 sides.

Answer 4

What are all the lengths of the left parallelogram?
Can you add the missing lengths to your figure?

Answer 5

14cm

Answer 6

In a parallelogram, opposite sides are congruent.

Answer 7

Ok, you know the perimeter of the left parallelogram and it is 14 cm.
That is correct.

Answer 8

Now what is the scale factor from the left to the right parallelogram?

Answer 9

Kinda confused

Answer 10

Look at the only side of the right parallelogram whose length we know.
It measures 4.5 cm.
Which side does it correspond to in the left parallelogram?

Answer 11

Okay, I got that.

Answer 12

Ok. You see that the right one is 4.5 and the left one is 3.
How many times bigger is the right one than the left one?
What is 4.5/3 = ?

Answer 13

1.5

Answer 14

Great.
Since one pair of corresponding sides has a scale factor of 1.5, that means every pair of corresponding sides has the same scale factor. Also, the perimeters have the same scale factor.

Answer 15

If you multiply any length o f the left one by 1.5, you get the length of its corresponding side on the right one.
The same is true for the perimeter. If you multiply the perimeter of the left one by 1.5, you get the perimeter of the right one.

Answer 16

so it'd be 4.5 and 5.5?

Answer 17

How did you get 5.5?

Answer 18

The scale factor works with multiplication, not addition.

Just like 3 * 1.5 = 4.5,

4 * 1.5 = 6

14 * 1.5 = 21

Answer 19

I see. Thank you.

Answer 20

You can do this problem 2 ways.

Method 1.
Find the scale factor: 4.5/3 = 1.5
The sides that are 3 at left become 3*1.5 = 4.5
The sides that are 4 at left become 4*1.5 = 6
Perimeter at right: 4.5 + 4.5 + 6 + 6 = 21

Method 2
Find the scale factor: 4.5/3 = 1.5
Find left perimeter: 3 + 3 + 4 + 4 = 14
Perimeter at right: 14* 1.5 = 21

Answer 21

You're welcome.