# How to find the area of a rectangle when only percentages are given? [closed]

That question goes like this 'If The larger sides of a rectangle are increased by 25% and the smaller sides are decreased by 20% , what is the area of the rectangle?' My original attempt was to assume the larger side as x and the smaller side as y but I couldn't find any possible solution to my approach.

I made up this question.

## closed as off-topic by projectilemotion, Jean-Claude Arbaut, Namaste, Juniven, LeucippusFeb 12 '17 at 1:17

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• Hint: $125\%=5/4\,$, $80\%=\cdots$ – dxiv Feb 11 '17 at 17:50
• I would suggest you to have a look at this – kishlaya Feb 11 '17 at 17:56
• I think I'm going to make a Desmos animation for this. Could be a fun challenge to try to program it – Brevan Ellefsen Feb 11 '17 at 18:08

I though I might add a bit of visual understanding to what is happening. Here is a (low framerate) Desmos graph that vizualizes your rectangle. Note that the area is invariant the whole time, i.e. the area doesn't change! I included gridlines so that you can count rectangles and confirm this for yourself.

• The visualization was helpful. Thank you! – Umer Qureshi Feb 11 '17 at 18:36

Area: $A=a\cdot b$
Note that $125\%=\frac{5}{4}$ and $80\%=\frac{4}{5}$
New area: $A=\big(a\cdot\frac{5}{4}\big)\cdot\big(b\cdot\frac{4}{5}\big)$
which is the same as $A=a\cdot b\cdot\frac{5\cdot4}{4\cdot5}$
the last term cancels $A=a\cdot b$

So the Area stays the same.

A rectangle's area can be calculated using the formula

$A = a \cdot b$

If we increase the one side, and decrease the other by the given percentage we get

$A = a \cdot 1,25 \cdot b \cdot 0,8$

When multiplying $1,25$ with $0,8$ we get

$A = a \cdot b \cdot 1$

This simply means that the area stays the same. It doesn't even matter if the shorter sides are increased or the longer ones are decreased, due to the Commutative Laws.