For any kite, we have two pairs of congruent adjacent sides. In general, the kite would have sides of x, x, y , y. In this case, x = 19 is known while y is unknown.
The four sides add up to 52, so
x+x+y+y = perimeter
19+19+y+y = 52
38+2y = 52
2y+38-38 = 52-38 .... subtract 38 from both sides
2y = 14
2y/2 = 14/2 ... divide both sides by 2
y = 7
Therefore the opposite side of the 19 meter side is 7 meters
