2TH §3.5 Mixed exercises

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§ 3.5 Mixed exercises today!

First let's look back at a difficult exercise from

§ 3.4:   exercise 30, page 112.

Open your Textbook!

Open your Notebook, too.

MAKE 30a now!

Answer to 30a What is the factor to multiply the sides of PQRS by to get KLMN, is ..........

1. √​9​​​
2. 3
3. 9
4. ​3​​1​​

Do you remember from §3.4 ?

When discussing two SIMILAR figures, then

- the dimensions are multiplied by, say k

- the perimeter is also multiplied by k, however

- the AREA is multiplied by 

k​2​​

30a The solution:

1st: calculate the factor to get from area PQRS to area KLMN.

That is 144 : 16 = 9

2nd: Take the ROOT of 9, to get the SCALE FACTOR from PQRS to KLMN

So: Root 9 = 3 = Scale Factor!

Now MAKE 30b in your Notebook!

30b The solution:

Let's keep it as simple as it can be.

(The Solutionsbook, normally very good, gives a pretty difficult solution...)

We make a table for the possibilities of the squares. 

We start with the area of 16 squared cm, because that has very few possibilities. Only 3, see next slide!

All possibilities follow here:

                            PQRS:                        KLMN:

1st:              1 cm x 16 cm         3 cm x 48 cm

2nd:            2 cm x 8 cm          6 cm x 24 cm

3rd:             4 cm x 4 cm          12 cm x 12 cm                            

Now a few questions about § 3.5,

today's homework.

Many exercises ask you to calculate the lengths of sides.
What is the best method for this?

1. Calculator
2. Make a ratio table
3. Hugging your neighbour
4. Comparing the angles

Now do § 3.5!

Exercises 33, 35 and 36 (page 114)

I want you to be COMPLETE in 33:

1. Calculate the unknown angles 

2. Draw the second picture in the same shape

3. Make a ratio table and fill in the matching lengths

4. Calculate the scale factor for the matching lengths

5. Conclusion: are the quadrilaterals similar or not?