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

Question

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.

Answer 1

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".

Answer 2

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%

Answer 3

Hi Juanelle;

Increasing anything by 100% is doubling it.

Area=(length)(width)

4(Area)=[2(length)][2(width)]

4=2x2

 

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)