The key here is to remember that if the figures are "similar", then
each pair of corresponding sides has the same ratio. In both problems,
the pair of figures is similar. (It says so twice on the sheet.)
For the triangle in #1):
-- One pair of corresponding sides is 15yd and 9yd.
-- Their ratio is 15/9 = 5:3 .
-- The other pair of corresponding sides is 20yd and 12 yd.
-- Their ratio is 20/12 = 5:3 .
-- For each pair of corresponding sides, the one in the small triangle
is 3/5 the size of the corresponding side in the big triangle.
-- The last pair of corresponding sides is 30yd and 'x' .
-- Their ratio is 5:3 . 'x' is 3/5 of 30yd.
For the quadrilateral in #3):
The figures are not both in the same position.
Compared to the smaller one, the bigger one is rotated
almost halfway around to the right.
The smaller one has the shortest side on the bottom, but
the bigger one has the shortest side almost on top.
So you have to be very careful about deciding which side of the
big one and which side of the small one are corresponding sides.
But the question does tell you that the drawings are 'similar', so
you know that each pair of corresponding sides has the same ratio.
-- One pair of corresponding sides is 12in (top of the big one)
and 4in (bottom of the small one).
-- Their ratio is 12/4 = 3 .
-- Another pair of corresponding sides is 30in and 10in .
-- Their ratio is 30/10 = 3 .
-- Another pair of corresponding sides is 36in and 12in .
-- Their ratio is 36/12 = 3 .
-- For each pair of corresponding sides, the one in the small figure
is 1/3 the size of the corresponding side in the big figure.
-- The last pair of corresponding sides is 48in and 'x' .
-- Their ratio is 3 . 'x' is 1/3 of 48in .
