If the dimensions of a rectangle become one-fifth of the original dimensions, then area of the new rectangle will be _______of the area of the original rectangle. Enter your answer in numerical form, using the / for the fraction bar if needed.

Question

anonymous · Answer

Call the dimensions of the rectangle x and y. Where x is width and y is height. Can you express the area of the rectangle in terms of x and y?

anonymous · Answer

@mjneedshelp if you ever get confused by these, since they did not give you the original dimensions, they do not matter.  therefore you are free to pick any you like, compute using the numbers, and whatever answer you get will be correct. i will give you an example

anonymous · Answer

If the dimensions of a rectangle become ONE THIRD of the original dimensions, then area of the new rectangle will be _______of the area of the original rectangle. Enter your answer in numerical form, using the / for the fraction bar if needed.

anonymous · Answer

with this slight change, i say, let the dimensions of the original rectangle by $3\times 3$ so area is $9$ 
why did i pick 3?  because one third  of 3 is 1
so my new rectangle has dimensions $1\times1$ and area $1$
you can see that my new area is one ninth the original area

anonymous · Answer

ok im confused

anonymous · Answer

repeat the process with ONE FIFTH instead and see what you get
then repeat again, this time using $5x$ instead of 5, and generalize

anonymous · Answer

area  goes with the square of the lenght
so if the original length is multiplied by 2, new area will be larger by a factor of 4

anonymous · Answer

if the original are is reduced by a factor of one half, new area will be reduced by a factor of $\frac{1}{4}$

anonymous · Answer

Algebraically (for satellite73's example), to work out the area of a rectangle you multiply the length and width together. If the width is x and the length is y, then the area will be xy. If we take instead the width to be x/3 and the length to be y/3 (so the dimensions have become one fifth the original) then we will multiply x/3 and y/3 together to get the new area. So the new area will be xy/9, which is one ninth the original area.
Now do the same for your question. State the measurements of the rectangle in terms of x and y, then divide them by 5 and find the new area in terms of x and y.

anonymous · Answer

the answer is 1/4 ?

anonymous · Answer

$$Area₁/Area₂ = \frac{ (⅕L)(⅕W)  }{ (L)(W) } = \frac{ 1 }{ 25}$$