Math Is Fun Forum

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Geometry question

Hi. I can't seem to find my way round this question, especially the (a) part; yet , I need it to answer the other sub questions. I'd app some assistance. Thanks.

In a diagram, PS//QR, PT//SR, |QR| = 24 cm, |SR| = |PT| = 18 cm, |PQ| = 20 cm and |PS| = 12 cm. Calculate, correct to 3 significant figures;
(a)  angle PQT;
(b)  the height of triangle PQT;
(c)  the area of PTRS as a percentage of the area of PQRS.

---

Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Geometry question

hi math9maniac

The key to many geometry questions is to get the right diagram.

I drew PS and QR parallel to it.  Then SR and PT parallel to it.  PXRS is a parallelogram where X lies on QR.  As SR = PT one interpretation of the information is that T = X.  The alternative is that T is on the other side of XP. I have shown this possibility as T'

But the usual convention when describing parallels is to preserve the directional sense which makes T where I have put it.  Also later the question talks about PTRS.  Again the convention is to take the points in the given order which confirms this interpretation.  If T is at T' then the shape PTRS crosses over itself and finding its area would be silly.

The dotted line shows you how to get the ratio of areas very simply.  You can get the angle using the cosine rule and the height with simple trig.

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

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Geometry question

Hi Bob;

Thanks for reply.

Here are my answers. Please verify whether I'm right or wrong. Thanks.

(a)  72.5 degrees
(b)  19.1 cm
(c)  66.7 %

---

Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Geometry question

hi math9maniac

Part c exactly!

Part a.  I don't get this.  Would you post your working out please.

Part b.  Would be correct if part a was correct, as it depends on it.

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

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Geometry question

Oh ok.

Interesting. Part c is correct, but not the others? I thought part c also depends on parts a and b.

---

Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Geometry question

Triangles PQT, TSP and STR are congruent, so that result follows whatever the other answers come to.

I've improved my diagram by making it accurately to scale and my calculated angle seems to be right.  If you show your working, I'll be able to see what is going wrong.

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

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Geometry question

Hello Bob;

I realise in your diagram that triangle PQT is right-angled; but this is quite impossible, considering the figures we have there  (20, 18, 12). In a similar diagram I tried, I have the sides PT and SR slanted; not perpendicular to line QTR as above. Could you consider that too? Could it be that?

---

Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Geometry question

A pipe of wire of lenght Lcm is bent into the shape of a rectangle. The area enclosed by the rectangle is 7.5cm squared.
i. If the length of the side of the rectangle is xcm, find an expression of L in terms of x.

Help please. Thanks

---

Only a friend tells you your face is dirty.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry question

Hi Bob & math9maniac;

I get a different shape from Bob's, which seems to have PQ=approx 25 instead of 20.

Also, I think I recall from school that the apex of a triangle in relation to its height is denoted by the middle letter (same as for an angle). If that's right, then "the height of triangle PQT" would be QB in my drawing.

Last edited by phrontister (2017-02-23 11:44:44)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry question

Hi;

You will need to upload that drawing to imgur to get others to see it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry question

I had uploaded it, but was in the middle of changing it. Fixed now.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry question

Hi;

I see it perfectly, thanks.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Geometry question

I realise in your diagram that triangle PQT is right-angled;

Where did you get that idea from.  There's no right angles in my diagram.

My diagram wasn't meant to be accurately drawn anyway but is like phrontister's.

Other problem:

Let the width be w, then L = 2x + 2w and xw = 7.5

So you can eliminate w and make L the subject.

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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry question

Hi Bob,

Sorry, I didn't mean to correct you where there was no need, but you did throw me earlier by saying that you'd improved your diagram by making it accurately to scale, and I hadn't understood what you meant by that.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry question

hi math9maniac

The key to many geometry questions is to get the right diagram.

I drew PS and QR parallel to it.  Then SR and PT parallel to it.  PXRS is a parallelogram where X lies on QR.  As SR = PT one interpretation of the information is that T = X.  The alternative is that T is on the other side of XP. I have shown this possibility as T'

But the usual convention when describing parallels is to preserve the directional sense which makes T where I have put it.  Also later the question talks about PTRS.  Again the convention is to take the points in the given order which confirms this interpretation.  If T is at T' then the shape PTRS crosses over itself and finding its area would be silly.

http://i.imgur.com/Be2T1zI.gif

The dotted line shows you how to get the ratio of areas very simply.  You can get the angle using the cosine rule and the height with simple trig.

Bob

Last edited by thickhead (2016-04-20 04:30:40)

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry question

Hi math9maniac;

"(b)  the height of triangle PQT;"

Do you know which of the three heights the question is asking for?

There are three options, and we're not told which side is the base or which point is the height vertex...and I haven't been able to confirm if what I wrote in post #9 about notation applies.

Last edited by phrontister (2016-04-21 11:21:58)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry question

Usually we start stating the triangle name with the vertex at the top second and third showing the base. So unless and otherwise stated the height means the perpendicular from first vertex.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry question

Thanks for clearing that up for me, thickhead...I hadn't been able to find out any information about that anywhere.

Btw, I think that in your previous post you meant PQT for the altitude, not PQR (as per the question)...but the answer would be the same.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson