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**samuel.bradley.99****Member**- Registered: 2016-03-16
- Posts: 51

How can we transform a parallelogram with sides n and 1.1*n into a rhombus of equal area, just by one cut?

*Last edited by samuel.bradley.99 (2016-10-14 06:21:56)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Equal surface? What does that mean?

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Maybe he means equal area.

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**samuel.bradley.99****Member**- Registered: 2016-03-16
- Posts: 51

Exactly, I corrected the wording. Sorry guys but English is not my mother tongue!!

zetafunc wrote:

Maybe he means equal area.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

Only in certain cases it can be done.If one of the diagonals has the dimension of a side either n or 1.1 n ,it can be cut along that diagonal and pasted on the other side.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi samuel.bradley.99

This works only if A lies on that circle. Still working on a general case.

AB = DC = 1.1n

AD = BC = n

Note AC = n, so the dotted diagonal will make the cut. Translate ADC (ie. Move it maintaining the parallel directions) so that DC fits over AB as the new diagonal.

The new parallelogram has four equal sides of size n, so it is a rhombus.

Bob

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**samuel.bradley.99****Member**- Registered: 2016-03-16
- Posts: 51

Thank you, but how about in the general case, where we don't know whether A lies on the circle?

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,462

hi samuel.bradley.99

General solution:

Draw parallelogram ABCD where AB = 1.1n and BC = n

With centre D and radius 1.1n, draw an arc to cut AB at E.

The cut required is along the line DE.

Remove the triangle coloured yellow, and move it to the position shown in orange.

AB = DC = EF = FC = 1.1n so EFCD is the required rhombus.

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 Bundy

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**samuel.bradley.99****Member**- Registered: 2016-03-16
- Posts: 51

Guys you are geniuses! Respect!!

Thank you so much!!

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