the area of ABCDE is 18 sq. cm.; the area of a similar pentagon PQRST is 32 sq.cm. the diagonal AC is 6 cm.; find the length of PR.

Answer 1

Assumptions:
1. ABCDE is also a pentagon
2. PR is the corresponding diagonal in the 2nd pentagon

In that case, the areas of similar figures are proportional to the square of their sides (or their diagonals)

PR^2/6^2 = 18/32
PR^2 = 648/32 = 81/4
PR = 9/2