word problem

Question

Each side of a square is lengthened by 8 inches. The area of this new, larger square is 144 square inches. Find the length of a side of the original square

Answer 1

Let x = the length of a side of the original square:  If we lengthen it by 8 inches, it becomes x+8.  The area of the new square is144 in²

 

      Area = (length of side)2

      144 = (x+8)²

      √144 = √(x+8)²

      ±12 = (x + 8)

 

Solve both cases, 12 and -12:

 

      12 = x + 8

      4 = x

 

      -12 = x + 8

      -20 = x

 

Since we can't have a negative length (-20), the answer is x = 4 inches.

 

Check:

      144 = (x+8)²

      144 = (4+8)²

      144 = 12²

      144 = 144

      Check!

 

- Phil in Olney