A Patch of Art

Geometry Level 1

A team of four designers came up with four designs to create a patch-work blanket consisting of identical squares:

Not being able to decide which is the best, they sewed the patches together in a cascading manner:

How many times is the area of the new patch larger than each of the old ones?

2 × 2 \times 4 × 4 \times 3 × 3 \times

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

Marta Reece
May 30, 2017

There are four areas where two of the patches overlap. They are the smaller squares in the middle of the pattern and their combined area is equal to that of one of the original patches. The new area is then 4 times the area of a single patch minus the area of overlap, that is 3 times the area of one patch.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

When reading the problem, I had a difficulty understanding what "new patch" meant, as it was not a shape easy to use as a patch. Perhaps something like "resulting shape" or some such would be more easy to understand.

Marta Reece - 4 years ago

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