SOLUTION: Please help. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find the length of the original square. Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find the length of the original square. Thank you.      Log On


   

Question 177383: Please help. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find the length of the original square.
Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = the length of the side of the original square.
If you increase this by 8 cm (s+8) and square it ((s+8)*(s+8)) you get 169 sq.cm. So you can write:
%28s%2B8%29%5E2+=+169 Square the left side.
s%5E2%2B16s%2B64+=+169 Subtract 169 from both sides.
s%5E2%2B16s-105+=+0 Factor this quadratic equation.
%28s-5%29%28s%2B21%29+=+0 Apply the zero product rule:
s-5+=+0 or s%2B2+=+0 which means that...
s+=+5 or s+=+-21 Discard the negative solution as the length of the sides can only be positive.
highlight%28s+=+5%29cm This is the length of the side of the original square.
Check:
%28s%2B8%29%5E2+=+169
5%2B8%29%5E2+=+169
13%5E2+=+169
169+=+169 OK!