Math Is Fun Forum

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Triangle Math Help

Hi, I need help solving these two problems. I've been stuck on them for quite some time.

I guessed on that one, but I figured it wouldn't hurt to get actual help.

What I've figured out from this one is:

Area of square: 144
Hypotenuse of triangle: 12

Please correct me if I'm wrong, thank you!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

hi

If you stay on-line, I'll prepare a reply for you.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

hi

If you stay on-line, I'll prepare a reply for you.

Bob

Sure, that's okay Thank you.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Hi again,

In the first one triangle KPN is 'similar' to KJQ.  That's because of the parallels.

That means that a constant scale factor will enlarge KPN to make KJQ.

You know 8 enlarges to 14, so the scale factor is 14/8

Apply the same to KN to get KQ

KQ = 16 times 14/8

Now subtract 16 to get NQ.

While you're trying that I'll look at the second one.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

Hi again,

In the first one triangle KPN is 'similar' to KJQ.  That's because of the parallels.

That means that a constant scale factor will enlarge KPN to make KJQ.

You know 8 enlarges to 14, so the scale factor is 14/8

Apply the same to KN to get KQ

KQ = 16 times 14/8

Now subtract 16 to get NQ.

While you're trying that I'll look at the second one.

Bob

So the answer IS 12?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Number 2:

The hypotenuse would be 12 if it's parallel to the 12, and/or the triangle has a 90 angle.  Sure looks like it but the questioner should have said so.  But you cannot do it otherwise, so let's assume so.

The area of a triangle is half base times height = 0.5 x 6 x 6√ 3.  Simplify that as a number x root 3 and subtract from 144.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

12 is correct for number 1. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

So for the second question, the answer would be C: 144 - 6√ 3

And the first question the answer is 12

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

12 yes.

But 0.5 x 6 x 6 is not 6.

Whoops!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

I chose C but that was incorrect.

I chose D but that was incorrect.

Please tell me the correct answer and how to do it and why its the answer! Thank you!

Last edited by Nickiekinz (2015-04-03 04:10:47)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

hi Nicole,

Complementary means add up to 90.

But read the question carefully.  It doesn't say the smaller is 35.  It says it is 35 smaller than the larger.  So call it x and the larger will be x + 35.

Then x + (x+35) = 90.

Oh.  where did that question go?  And did you sort out the shaded area?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

Yes, I just figured that out! I've correct 4/6 of them so far. All of them were wrong because I jumped the gun and didn't completely read the question..oops!

I just have two more I cannot figure out.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Q8.  No letters so I'm not sure which is A and which is B.

Q12.  Imagine you are a little ant walking around the perimeter of a polygon.  As you reach a corner you have to turn through one exterior angle to continue along the next side.  When you have completed the walk you have turned around 360.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

So for question 12, the answer is C? The square and the polygon both have the exact sum of exterior angles.

As to question 8..that would be because I uploaded the wrong picture!

Here is the correct one.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

For number 8 I think the correct answer is D because we don't have any measure of B or A  so we don't know if they're both 45 degrees or different numbers. Right?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Q12.  C is correct. 

Q8.  In any triangle the largest angle is opposite the largest side; the next largest angle is opposite the next largest side; and the smallest angle is opposite the smallest side.  For me, it is obvious that BC is the smallest but, strictly, I can only prove that by doing a Pythagoras calculation.  If I had a student who said B, I'd be happy to give them the marks, but you probably ought to say D.  Is this Compu-High by any chance?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

I'll choose D and see what happens

And yes, it is Compuhigh

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

If you could also help me with the general proofing questions, that would be awesome!

14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.

A Given
B Definition of an inscribed angle
C Unfounded
D Properties of a central angle
E Properties of an arc
F Definition of radius

I chose E (incorrect)

15. The area of a sphere is 4 times the area of a circle with the same radius.

A Given
B Definition of a radius
C Definition of a circle
D Definition of a sphere
E Formula for area of a sphere
F unfounded

I chose D (incorrect)

18. If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53).

A Distance Formula
B Definition of a point
C Definition of a distance
D Definition of a line
E Definition of coordinates
F Definition of radius

I chose C (incorrect)

Last edited by Nickiekinz (2015-04-03 04:34:13)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Thought I recognised their unique style of question.    Good luck.  Got to go now.  bye.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

Oh sorry just seen the next ones.  I'll look at them in about one hour.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: Triangle Math Help

It's okay, it was from a previous lesson and I got a 9 out of 10 score on it, haha. I still have an A in the class so I think I'll live if I don't correct them to get a 10, thank you though!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,155

Re: Triangle Math Help

hi Nicole,

These questions are a good example of one of the things I dislike about Compuhigh.  If you are going to set a multi-choice question (and I have; as a teacher and an examiner), then you must make sure that, to a student who knows the work, one answer is clearly right and the others clearly wrong.  I cannot imagine that any of these would get through the very careful, independent scrutiny that all exam questions get in the UK.

14. If a central angle is 30 degrees, then the arc it defines is also 30 degrees.

A Given
B Definition of an inscribed angle
C Unfounded
D Properties of a central angle
E Properties of an arc
F Definition of radius

I chose E (incorrect)

My answer would depend on how they have defined 'the arc it defines'.  It could be A. given, if the arc angle definition is 'the angle made by an arc at the centre'.  It could be D, properties of a central angle, for the same reason.  Or E, properties of an arc, if that's how an arc is defined (less likely).  If E is wrong, my guess (and it would be a guess despite being very good at geometry) would be to try  A or D.

15. The area of a sphere is 4 times the area of a circle with the same radius.

A Given
B Definition of a radius
C Definition of a circle
D Definition of a sphere
E Formula for area of a sphere
F unfounded

I chose D (incorrect)

You couldn't prove this without knowing what a radius is, and a circle, and a sphere, but they were probably expecting E, the formula for (^surface) area of a sphere

18. If I have two points, (-2, -3) and (-4, 4) then the distance between them is sqrt(53).

A Distance Formula
B Definition of a point
C Definition of a distance
D Definition of a line
E Definition of coordinates
F Definition of radius

I chose C (incorrect)

Again you need to know what a point, a distance and coordinates are.  But they probably wanted you to say A, distance formula.

If you decide to re-submit, please let me know what was right.  .

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob