SOLUTION: Can you please help me on this problem. I dont get it. A corner lot that originally was square lost 185 m^2 of area when one of the adjacent streets was widened by 3 m and the o

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help me on this problem. I dont get it. A corner lot that originally was square lost 185 m^2 of area when one of the adjacent streets was widened by 3 m and the o      Log On


   

Question 162235: Can you please help me on this problem. I dont get it.
A corner lot that originally was square lost 185 m^2 of area when one of the adjacent streets was widened by 3 m and the other was widened by 5 m. Find the new dimensions of the lot. (Hint: Let x= the length of a side of the origanal square lot.)
Sincerly,
Very confused student
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, first the lot was a square with side, x.
Its original area was x%2Ax or A%5Bo%5D=x%5E2.
The street was widened on one side, that x shrunk by 3, so it's now (x-3).
The other side street was widened and that side shrunk by 5, so it's now (x-5).
Now instead of a square, you have a rectangle.
The new area is A%5Bn%5D=%28x-3%29%28x-5%29.
You know that you lost 185 in from old to new area.
A%5Bn%5D=A%5Bo%5D-185
Substitute with variable expression for areas.
%28x-3%29%28x-5%29=x%5E2-185
Use the FOIL method on the left hand side,
x%5E2-5x-3x%2B15=x%5E2-185
-8x%2B15=-185
-8x=-200
highlight%28x=25%29
.
.
.
The original lot was 25m x 25m (625 m^2).
The new lot is 22m x 20m (440 m^2).