Math Is Fun Forum

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Difficult geometry prob

Hi,
ABCD is a square. Parallel lines m, n, and p pass through vertices A, B, and C, respectively. The distance between m and n is 12, and the distance between n and p is 17. Find the area of square ABCD.
Im trying to post an image but it wont let im new

thanks I spent I couple hours on this and have no idea.
-thedarktiger

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Difficult geometry prob

hi thedarktiger,

Welcome to the forum.

You'll get picture posting rights when you've been a member for a while.

Hopefully the one below is your problem.

Look at the angles I've marked x and y.  They add to 90 and you'll see other angles of the same size in the diagram too.

So show that triangles ABE and BCF have the same angles and one side equal so they are congruent.

Then use Pythagoras to get a side.

Bob

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Difficult geometry prob

Hi;

---

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: 10,643

Re: Difficult geometry prob

hi

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Difficult geometry prob

Hi Bob;

---

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: 10,643

Re: Difficult geometry prob

hi bobbym,

I did it with:

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Difficult geometry prob

Hi;

---

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.

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: Difficult geometry prob

Hi,
thanks a ton I got 433 (how to hide?) after you guys
I was clueless!
EDIT:
im a bob to im robert!

Last edited by thedarktiger (2014-01-11 17:33:13)

---

Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Difficult geometry prob

hi Bob,

433 looks good to me.

To hide:

square bracket hide="optional message in box"  square bracket  "what you want to hide here" then end with square bracket /hide square bracket.

For me, the key to the solution was when I drew the lines AE and CF.  The software I use (Sketchpad) lets me put on lines that are truly parallel and maintains all the 90 angles.  So I was able to experiment by varying the parallels.  It looked like AE = BF so I thought I'd try to prove it.  Then everything fell into place nicely.

With geometry I usually find the diagram is the key thing.  Get that right and the route to an answer often becomes visible.  I needed to put on two lines to show the 12 and 17 distances and it seemed it would keep things simpler if I drew these from A and from C. 

Hope that helps. 

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