Can you please help me solve this problem> If each of the dimensions of a rectangle is increased by 100% , by what percent is the area increased.

There is an important difference in the ways the new area could possibly be stated.

The new area is 4 times what it was before.

2L x 2W = 4LW

So the new area is four times the old area of LW

or 400% of the old area.

But the increase in area is 300%

Increase is looking for the difference between the old and new.

4LW - LW = 3LW increase

So the increase in area is 3 times what the old area was

or the increase in area is 300%.

Since according to your question you are asked for the
percent increase,

the answer would be "the area is increased by 300 precent".