Math Is Fun Forum

Krash

Member

Registered: 2015-04-18

Posts: 1

Geometry Help!

Q1)
Find AC in the following triangle, to two decimal places.

Q2)
Find BC in the following triangle, to two decimal places.

Q3)
In the diagram, PQRS is a trapezoid with base \overline{PQ}. Median \overline{MN} intersects the diagonals at X and Y. If SR = 12 and XY = 3, find PQ.

Thanks!

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: Geometry Help!

Hi krash;

Q1. use the rule AC² =AB² +BC² -2AB.BC.Cos(B)

AC² =9+1-2(1)(3).Cos(40)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry Help!

hi Krash,

Welcome to the forum.

And Q2 needs the sine rule:

Q3.  Because MN is half way between SR and PQ there are lots of similarity properties you can use here:

MX = ½ SR = YN

MN = ½ (SR + PQ)

MY = ½ PQ = XN

I think that's enough to work out PQ.

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

ET ag

Member

Registered: 2017-02-22

Posts: 10

Re: Geometry Help!

Hi Krash,

Given what was said above and the similarities that Bob gave, we get MX as 6, and we know that XY is 3. This shows that MY = 9, thus PQ = 18.

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If a second was a minute, and a minute was an hour, how many hours would be in one day? (There are multiple answers and they are debatable)

adpqadpq

Member

Registered: 2017-02-03

Posts: 18

Re: Geometry Help!

Can somebody give me some help on Q3? Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry Help!

hi adpqadpq

The two posts above yours suggest a method.  Have you tried and how far did you get?

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

adpqadpq

Member

Registered: 2017-02-03

Posts: 18

Re: Geometry Help!

Should I use the sine rule for Q3?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry Help!

Should I use the sine rule for Q3?

Are we looking at the same question?  I'm seeing a trapezium PQRS with MN half way between the parallel sides.

This is what I said in 2015

MX = ½ SR = YN

MN = ½ (SR + PQ)

MY = ½ PQ = XN

and I cannot improve on that now.  I wouldn't use the sine rule as I don't know any angles.  With the method I am suggesting I can do it in my head even at 01.05 BST.

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

adpqadpq

Member

Registered: 2017-02-03

Posts: 18

Re: Geometry Help!

Never mind, i got the correct answer. it is 18