Math Is Fun Forum

lewis demeniminator

Guest

Urgent Help!!! D;

hi,, can someone plaesa help me with this question. ive been stuck on it for 2 months!!!! it is so confuddling :S
here it is:
  there is a point X inside a square, PQRS, such that PX=1, QX=2 and triangles PXQ and PXS are congruent. What is the area,in square units of the square?

i will do 150 push ups if someone can get the answer. 

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Help!!! D;

Hi lewis demeniminator;

I am geting that the point is at:

And the side s of the square is:

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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.

lewis denimenimator

Guest

Re: Urgent Help!!! D;

thanks.. but what about some working?
i do not understand how you reached that answer :S
im sorry im so stupidd

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Help!!! D;

Did you do the pushups?

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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.

lewis denimenimator

Guest

Re: Urgent Help!!! D;

bahahahahaha,,, i will once you give me the working out.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Help!!! D;

Hi;

I solved the problem using analytical geometry. PXQ and PXS are given and obviously congruent by SSS, also given. We are looking for side s.

See the diagram below.

We do not know what the 3 variables x , y and s equal.. We will get them from simple applications of pythagoras. We start by forming 3 simultaneous equations:

The first triangle PAX is:

The second triangle AQX is:

The third triangle PXB is:

We have 3 eqtns. to solve:

We can eliminate y and get:

and

Solve for x:

Plugging into the second eqtn.

You get y by plugging into any one of the original equations.

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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.

MathsPersonOkay

Member

Registered: 2016-05-04

Posts: 2

Re: Urgent Help!!! D;

Hey Bobbym, I was wondering if you could explain the simultaneous part for me again. I have basic knowledge about it but don't quite understand it here. Thank you.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Help!!! D;

Hi;

What is is exactly where you are stuck?

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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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Urgent Help!!! D;

Because of congruency of  triangles X lies on diagonal PR. Let PX extended meet SQ at T.

Last edited by thickhead (2016-05-04 16:29:57)

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