Math, Algebra help Area related question

Can someone explain what i need to do for
this equation please
http://i.imgur.com/YWhER.png

You need to set up a pair of equations with two unknowns x and y
the first equation is given as area
A = xy
6000 = xy

The other equation is for the perimeter
this will be adding up all the sides less the amount cleared by the building

x + (x-10) + y + (y-10) = 334
simplifies to
2x + 2y -20 = 334
or
2x + 2y = 354
divide by 2
x + y = 177

This gives you two equations and two unknowns which you may solve on your own. If this is also an unknown area, I have solved it below

if you solve this second equation for y

x = 177 - y

now substitute this x into the other equation
6000 = xy
6000 = y(177 - y)
6000 = 177y - y^2
or
y^2 - 177y + 6000 = 0

using the quadratic equations

y = (177 +_sqrt (177^2 -4(1)(6000)) / 2(1)
y = 177 +_85.61 / 2

y = 131.3 or y = 45.7

a little checking will reveal that these two numbers are our x and y dimensions and can be interchanged without violating any of the conditions of the problem