SOLUTION: A square field had 5 meters added to the length and 2 meters to its width. The field then had an area of 130 meters squared. Find the length of a side of the original field.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A square field had 5 meters added to the length and 2 meters to its width. The field then had an area of 130 meters squared. Find the length of a side of the original field.      Log On


   

Question 319980: A square field had 5 meters added to the length and 2 meters to its width. The field then had an area of 130 meters squared. Find the length of a side of the original field.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A square field had 5 meters added to the length and 2 meters to its width.
The field then had an area of 130 meters squared.
Find the length of a side of the original field.
:
Let x = side of original field
then
(x+5) = the new length
and
(x+2) = the new width
:
L * W = 130
(x+5)(x+2) = 130
FOIL
x^2 + 2x + 5x + 10 = 130
:
x^2 + 7x + 10 - 130 = 0
:
x^2 + 7x - 120 = 0
Factor
(x + 15)(x - 8) = 0
The positive solution is what we want here
x = 8 meters, side of original square
;
:
Check solution by finding the area of the new rectangle
(8+5)*(8+2) = 130