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Below is the theorem tried proving geometrically in book

"Mathematics for Computer Science

Eric Lehman and Tom Leighton

2004"

**False Theorem 11. 420 > 422**

My question:

I would like to know the error in proof

Sham

Sham

Below is the theorem tried proving geometrically in book

"Mathematics for Computer Science

Eric Lehman and Tom Leighton

2004"

My question:

I would like to know the error in proof

Sham

Sham

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>2 mentioned for length of both new triangles is wrong?

It is <2

But I feel length of new traingle is more than 2 for both traiangles, Because length of rectangle is greater than breadth.

Sham

If breadth of 2 new triangles is 2 units, then length of 2 new triangles will definetely be > 2 units.

Sham

length of triangle will be > 20 if breadth of triangle is 20

Because length of any rectangle is obviously greater than breadth of rectangle.

Sham

Cut it in half diagonally to get two triangles w= 21 and h= 20.

Now cut the the little corner triangles with w= 2.

You should do the calculations. It's not that hard.

Why estimate a length as >2 when you can calculate it exactly???

There is a simple similar triangle ratio calculation that will tell you the answer.

You can do it in your head. But you do have to do it.

http://www.cs.princeton.edu/courses/archive/spr10/cos433/mathcs.pdf

Why

The upper pience is moved left exact 2 units.

After shift, If i consider any one triangle,

what i understand is horizontal length is 2 units and vertical length is definitely less than 2 units because upper piece was shifted horizontally and the horizontal length is 21 > vertical length 20

But How do i calculate second side of triangle if you do not know hypotenus ?

Sham

but

"20/21=x/2" is going above my head

i did not understand this

Sham

You may need to do some reviewing.

http://www.mathopenref.com/similartriangles.html

The base of the small, similar triangle is 2. The ratio of the heights to bases will be the same.

```
Height 20 X
------ = ---- = ---
Base 21 2
Cross multiply to find 21*X = 20*2 ==> X = 40/21
```

I sincerely remembernow that idid such exercise in school days 18 -20 years back.

you basically took big triangle and small triangle from any one piece.

But i strongly feel there is one theorem based on which you wrote this.

What was that theorem

Sham

I feel you wrote

20/21 = x/2

based on one theroem

Because this idea is not intuitive

What is that theorem

Sham

Properties of Similar Triangles

Corresponding angles are the same.

Corresponding sides are all in the same proportion.

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Start your 7-day free trialI accept this answer,

But before that, I would like to ask one question which is beyond this discussion,

I read this property in my school days.

How do you prove the following?

Properties of Similar Triangles

Corresponding angles are the same.

Corresponding sides are all in the same proportion.

Sham

Math / Science

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