enlargement scale factor root 2

a shape is shown
enlarge it by a scale factor that is the square root of 2
one of the shorter lengths or the shortest length is shown

then enlarge by this scale factor again
again a/the shorter/shortest length is shown
the shapes should not overlap with the original or each other

this can be done or confirmed by dissecting the shapes into simpler shapes (e.g. right angled triangles)
or you can use pythagoras and multiply surds

students can compare the areas of the original and enlarged shapes

a previous version of this task seemed difficult: