How to find the area of a rectangle when only percentages are given?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.