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If each of the dimensions of a rectangle is increased by 100% by what percent is the area increased

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3 Answers

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".
100% = 1
A = length * width

"... if each of the dimensions of a rectangle is increased by 100% ..."

Let length of new rectangle be "l1" and width - "w1"

l1 = l + l * 100% = l + l * 1 = 2l

w1 = w + w * 100% = w + w * 1 = 2w 

A1 = 2l * 2w = 4lw = 

lw + 3lw =

A + 3A =

A + 300% * A

Thus, the area is increased by 300%
Hi Juanelle;
Increasing anything by 100% is doubling it.
Let's try a hypothetical example.
A rectangle is 4 units x 3 units.
Its area is 12 units-squared.
We will increase both dimensions by 100%.  We will double each of these.
It is now 8 units x 6 units.
Its area is 48 units-squared.
Its increase is 4x2=(2x2+2x2)