What is, the answer to this problem

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 .

5/8 beds for each square yard