Question 521326
Hey the previous tutor gave you the correct answers but the steps are totally missing... So in case you're still left in the dark i'll give you my 2 cents

Okay!
So lets call the longer side "x" and the shorter side "y"
Regardless of which is length or width the formula is the same. 

Area = length x width

Therefore Area = xy

The question says that the original area is 270cm^2
So xy = 270cm^2

*NB
Keep in mind, we can manipulate this equation as we have a like depending on what we need so 
x = 270\y
and
y = 270\x
Get it? Got it? Good
Alright moving on!!

So the question tells you to increase the longer side (x) by 4cm and to decrease the shorter side (y) by 2 cm and the 'new' area will increase by 16cm^2
So in a form we can actually use, this basically means:

(x+4)(y-2)=270+16
(x+4)(y-2)=286

Alright so we'll expand this (i'm gonna assume that you know how to expand)and then we'll get
xy-2x+4y-8=286

Still with me? Alright kl

So in order to work this with a quadratic formula we need to change some stuff around
Remember back when i said that although 270 = xy we can alter it as we see fit to get what we need?
Yeah .. if you don't i suggest scrolling back up cause this is where it comes in
(^.^)

x = 270\y
and
y = 270\x

For this equation i'm gonna write y in terms of x which is this thingamajiggy below:
y = 270\x
and inject it into the equation

Stay with me

so instead of this:
xy-2x+4y-8=286

I get this:
x(270\x)-2x+4(270\x)-8=286

We have to simplify that first and get
270-2x+1080\x)-8=286

And then put everything as a fraction of x( as in make x the denominator by multiplying everything on the left side of the equation except '1080" by x
So we're left with
(270x-2x^2+1080-8x)\x = 286

Alright. I always hated fractions... ugh so lets get rid of the x denominator by multiplying both sides by x. This cancels out the x denominator and multiplies the 286 by x on the left side of the equation.

270x-2x^2+1080-8x= 286x

Let's switch things up a bit so it looks more like a quadratic equation

-2x^2+270x-8x+1080=286x

All quadratic equation need to be equal to zero before we can implement the formula so subtract 286x from both sides

-2x^2+270x-8x+1080=286x-286x
-2x^2+270x-8x+1080-286x=0

That gives us
-2x^2-24x+1080=0

So FINALLY  we can use the quadratic formula to solve the equation

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

*[invoke quadratic "x", -2, -24, 1080 ]



Whether you used the quadratic solver i so lovingly offered or did it by hand or calculator or prayer, your answers should be 
x=18 or x= -30

Distance can't be negative so the -30 is useless to us. 
Now what we focus on is the POSITIVE 18!!

So with x=18
We draw for the old equation
 xy=270
Now that we know what x is its now
18y=270
y=270\18
y=15


REALLY HOPE THIS HELPED... I KNOW ITS LONG BUT IT SHOULD GET THE JOB DONE 
=)