1

Part of 2009 Swedish Mathematical Competition

Problems(1)

5 square carpets in a square hall, can they fit in without overlaps?

Source: 2009 (-10) Swedish Mathematical Competition p1

Five square carpets have been bought for a square hall with a side of

6

m , two with the side

2

m, one with the side

2.1

m and two with the side

2.5

m. Is it possible to place the five carpets so that they do not overlap in any way each other? The edges of the carpets do not have to be parallel to the cradles in the hall.

geometrySquaresareas