SOLUTION: If the sides of a square are lengthened by 6cm the area becomes 169cm^2. Find the length of a side of the original square? I do so have a tough time deciphering word problems, and

Question 163887: If the sides of a square are lengthened by 6cm the area becomes 169cm^2. Find the length of a side of the original square?
I do so have a tough time deciphering word problems, and need some help please.
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the side of the original square in cm
The problem says
cm2
or

Take the square root of both sides

The side of the original square is 7 cm
check:
cm2
cm2

OK
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Area of original square:

where A is the area and s is the side length

Since "the sides of a square are lengthened by 6cm the area becomes 169cm^2", this means that we replace A with 169 and s with to form the area of the enlarged square. So we get:

FOIL

Subtract 169 from both sides

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for s

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, since a negative length isn't possible, this means that the only answer is
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