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Question 325506: If the sides of a square are lengthened by 3 km, the area becomes 81 square kilometers.Find the length of the original square
Found 3 solutions by rfer, info@email-tutors.com, MathTherapy:
Answer by rfer(16322)   (Show Source):
Answer by info@email-tutors.com(9)  (Show Source):
You can put this solution on YOUR website! The length of the original square was 6 km. Here is why:
6+3 = 9
9 squared = 81
You can also solve it algebraically. The area of the square is 81. Let "x" be the original length. If "x+3" is the new length, then "x+3" squared would be equal to 81. "x+3" squared is x^2 + 6x + 9 = 81
subtract nine from both sides to get: 72 = x^2 + 6x
use the quadratic formula, and you will get "6" as your solution.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! If the sides of a square are lengthened by 3 km, the area becomes 81 square kilometers.Find the length of the original square
Let one side of original square be S
Since a side of the new, lengthened square is 3 km greater than one side of the original square, then one side of the new, lengthened square is S + 3
Since the new, lengthened square has an area of 81 sq. km, then we'll have:
(S + 3)(S + 3) = 81
(S + 12)(S - 6) = 0
Therefore, S, or one side of original square is either -12, or 6, but since we CANNOT have a negative measurement, we IGNORE S = - 12, which leaves one side of the original square:  km.
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