22. Four copies of the triangle shown are joined together, without gaps or overlaps, to make a parallelogram.
What is the largest possible perimeter of the parallelogram?
A $46 \mathrm{~cm} \mathrm{~B} 52 \mathrm{~cm}$ C $58 \mathrm{~cm} \quad$ D $62 \mathrm{~cm} \mathrm{E} 76 \mathrm{~cm}$
22. $\mathbf{E}$ In order to join the four triangles together it is required to join together at least three pairs of edges, which consequently are not part of the perimeter of the resulting parallelogram. The four triangles have a total of 12 edges, so the maximum number of edges which
can be part of the perimeter of the parallelogram is $12-3 \times 2=6$. For the perimeter to be as large as possible, all four $13 \mathrm{~cm}$ edges should be included together with two of the $12 \mathrm{~cm}$ edges, if this is possible. The diagram shows how it may be accomplished. So the largest possible perimeter is $(4 \times 13+2 \times 12) \mathrm{cm}=76 \mathrm{~cm}$.