Your assumption is that the length is increased by x meters, the increased length is (100+x) meters, and the corresponding increased width is 300-( 100+x)=200-x meters.

Your two equations are x=0 or x= 100.

When x=0, the increased length is100+0 =100m, and the increased width is 200-0 = 200m. At this time, it is obviously not true that the length is less than the width, so x=0 does not meet the meaning of the question.

When x= 100, the increased length is 100+ 100 = 200m, and the increased width is 200- 100 = 100m.

Be content to grow wider than others and meet the meaning of the question.

To sum up, when the playground covers an area of 20,000 square meters, the corresponding length is 200 meters and the width is 100 meters. At this point, x= 100.