Geometry review

zee-f · 2012-12-15 04:16:10

Hi,

I got C as an answer wondering if that is correct

7. The apothem of a regular 9-sided figure is 6 feet and the area is 117.67 square feet. What is the perimeter of the regular 9-sided figure?

A 4.36 feet
B19.61 feet
C39.22 feet
D54.00 feet

anonimnystefy · 2012-12-15 05:12:37

C is correct. Good work!

zee-f · 2012-12-15 05:56:52

Thanks

zee-f · 2012-12-15 05:57:53

and for this one I choose A

9. What is the value of x?

A 22.5
B 45
C 63.6
D 50

Last edited by zee-f (2012-12-15 05:58:30)

anonimnystefy · 2012-12-15 06:12:13

Hi

That is not correct.

Bob · 2012-12-15 06:40:27

hi zee-f

What sort of triangle is ABD (yes right angled but what else ?)

Bob

zee-f · 2012-12-15 08:30:37

Isosceles Triangle?

Bob · 2012-12-15 09:14:38

Correct ... and therefore x = ?

Bob

zee-f · 2012-12-15 10:34:55

45?

Bob · 2012-12-15 10:53:35

Yes, that's it.

Bob

zee-f · 2012-12-15 11:19:31

Thank you

Still working on the rest 11 left

Bob · 2012-12-15 11:20:27

OK. You know where to come if you are stuck.

Bob

zee-f · 2012-12-15 11:24:31

Ok So can I cut the trapezoid into a square and a right triangle?
So the triangle side would be 8

10. In the diagram shown,line PN is parallel to line JQ , KN =16 centimeters, PN= 8 centimeters, and JQ = 14 centimeters. Determine the length of line NQ.

A 28 cm
B 12 cm
C 9.1 cm
D 7 cm

Bob · 2012-12-15 11:28:21

Triangle KJQ will have the same angles as KPN.

So it is an exact enlargement (do you say dilation?)

So you can use 8 ----> 14 to work out the scale factor

and apply to 16 ----> KQ

Bob

zee-f · 2012-12-15 11:41:08

So I can use the Pythagoras theorem

14²+ b²= 16²
196+ b² = 256

256- 196=b²
b²= 60
b= 2√15 or 7.75

Bob · 2012-12-15 11:52:49

You don't need Pythag. It is simpler than that.

In my diagram, I've split away the larger triangle so you can see the enlargement effect more clearly (I hope).

So 8 gets enlarged to become 14. That's a scale factor of x 14/8

Apply the same scale factor to 16 and you will get KQ.

Youi'll still have to do a subtraction to get NQ

Bob

ps. You are not told there is a right angle so that's another reason for avoiding Pythag. I know it looks like 90 but it might not be.

zee-f · 2012-12-16 00:21:21

a bet confused because I don't remember taking dilation but
triangle KPN I get the following information :

opposite = 13.8564
hypotenuse = 16
adjacent = 8

and I get a 90 60 30 angle

Bob · 2012-12-16 00:26:07

hi zee-f

http://www.mathisfunforum.com/viewtopic.php?id=18566

post 6

Give me a moment and I'll come up with a better explanation for the latest problem.

Bob

Bob · 2012-12-16 00:52:10

Right. One step at a time.

(i) Why you cannot use Pythagoras' theorem:- That angle that looks like 90 degrees may not be. The question doesn't say it is. Maybe it is 89 ?

And even if it is, working out KP doesn't get you any nearer to working out NQ.

(ii) This is a problem about enlargement, not Pythagoras. On the MIF teaching pages it is called 'Resizing'.

Have a look at

http://www.mathsisfun.com/geometry/resizing.html

I think you must have done it because it was on the transformations thread.

Have a look at both links and make sure you are clear about that.

(iii) I've taken your diagram and tried to show how the points J and Q are made by stretching the shape away from the centre at K.

P is stretched to J and N is stretched to Q.

A transformation like that is what I call an enlargement. But on your transformation thread the question said dilation, and bobbym used the same word, so maybe that's just the difference between UK english and USA english.

Whatever, my point is:- the triangle KPN has got bigger and the new bigger triangle is KJQ.

If it had got twice as big the scale factor would be x2. Three times as big would be x3.

In this problem it isn't as much as x2 because JQ is only 14 not 16.

So how can you work out the scale factor this time.

So

and then

Bob

zee-f · 2012-12-16 03:41:21

ooooh yeah from the Transformation lesson forgot about that

KQ= 16 * 14/8
KQ= 28

NQ= 28 - 16

NQ = 12

zee-f · 2012-12-16 04:33:40

Thank you

zee-f · 2012-12-16 05:21:52

I submitted my work I got 12/20 So 8 wrong

zee-f · 2012-12-16 05:45:17

I choose B because Complementary angles are two angles whose measures total 90 degrees.

90 - 35 = 55 and it was incorrect.

1. Two angles are complementary. The smaller angle is 35° less than the larger angle. What is the measure of the larger angle?

A- 27.5°
B- 55°
C- 62.2°
D- 125°

Bob · 2012-12-16 06:47:50

hi zee-f

NQ = 12 is what I what I got too.

Complementary angles add up to 90

The question doesn't say "Two angles are complementary. The smaller angle is 35°. What is the measure of the larger angle?

It says "Two angles are complementary. The smaller angle is 35° less than the larger angle. What is the measure of the larger angle?

Do you see the difference?

So if the larger one is x the smaller one is (x-35) and together they add up to 90.

Bob

zee-f · 2012-12-16 08:43:04

So the equation would be x + y - 35 = 90 right?

Math Is Fun Forum

#1 2012-12-15 04:16:10

Geometry review

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Re: Geometry review

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