Q.

[khalil]

One side of a rectangle is three times the other. If the perimeter increases by 2%, what is the percentage increase in the area?

[kamil9876]

P=3x+x+3x+x
=8x

let ' mean new thing, ie: P' means new perimeter etc.



(1)

so x also increases by 2%.

However:




sub in (1) and expand the square:




So the area was multiplied by a ratio of

which is percent. However converting it into "how much percent it increased by" We have ot subtract 100%.(ie. just like increasing by 2% means multiplying by 102/100, we're going backwards now)

So in the end its like 4.04%

Note: I have assumed that the 3:1 ratio of length to width is preserved even after this increase of Perimeter. Which you havn't meant clear but the question probably said though, otherwise there would be no answer.

[khalil]

thanks Kamil, you've taken a Further maths approach to it, but never mind it yields the correct answer!