SOLUTION: A rectangular skating rink has length 22m and width 30m. The rink is made larger by extending the width and length by the same amount such that the area of the new rink is 825 m^2.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular skating rink has length 22m and width 30m. The rink is made larger by extending the width and length by the same amount such that the area of the new rink is 825 m^2.      Log On


   

Question 395297: A rectangular skating rink has length 22m and width 30m. The rink is made larger by extending the width and length by the same amount such that the area of the new rink is 825 m^2. Create a quadratic equation to models this situation and use it to determine the new dimensions of the new rink.

Note: the length of one side and the width of one side, not all the way around.
Please help me.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular skating rink has length 22m and width 30m.
The rink is made larger by extending the width and length by the same amount
such that the area of the new rink is 825 m^2.
Create a quadratic equation to models this situation and use it to determine the new dimensions of the new rink.
:
Let x = amt added to the length width to get an area of 825 m/sq
:
The area equation using the new dimensions:
(x+22)(x+30) = 825
FOIL, subtract 825 from both sides
x^2 + 30x + 22x + 660 - 825 = 0
:
x^2 + 52x - 165 = 0
you can use the quadratic formula, but this will factor
(x + 55)(x - 3 = 0
The positive solution
x = 3 meters added to each dimension
:
The new dimension: 33 by 25
:
See if that is true
33 * 25 = 825;