Using one straight cut, divide this triangle in two pieces. Paste them together to form a parallelogram with perimeter 19.

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## Solution

We consider the general case of a triangle with sides a, b and c. Cut parallel to side a through the midpoints of sides b and c. Then reflect the upper triangle in the c-midpoint as shown.

Since the horizontal parallel line segments have equal length, the connecting line segments are also parallel. Thus we have made a parallelogram with two sides of length a and two of length b/2. Its perimeter is 2a+b.

We could also have mirrored the upper triangle to the left. Also we could have cut parallel to b or c. So we have six possibilities having perimeters 2a+b, 2a+c, 2b+a, 2b+c, 2c+a and 2c+b. In case a=7, b=5 and c=6, we can see that both 2a+b and 2c+a equal 19. The first case is shown above.

## Poem

The first cut

From a masterpiece

Can be a lot today

A painting or a writing

For a star’s shining

For a child’s loving

The love and inspiration

And even the protection

Also deep creation

And in my eyes

A sculpture

The first cut

A bright piece, a scintillation.