## anonymous one year ago If a square has an area of 4x^2-2xy +49y^2 sq cm. Find the length of its side and solve its perimeter. Please help, am I going to use 'completing the square'? Thanks!

1. phi

the area of a square is s*s (where s is the length of its side) that is, s^2 so I would expect the expression 4x^2-2xy +49y^2 to be a perfect square are you sure it is really -2xy for the middle term ?

2. anonymous

yeah its -2xy :((

3. phi

in that case, I would just say the side has length $s = \sqrt{4x^2-2xy +49y^2}$ and the perimeter is 4s, so $4\sqrt{4x^2-2xy +49y^2}$

4. anonymous

ohh, okay2 thanks! :)

5. Loser66

if x =1, y =2 we have the expression = 14^2 , but not sure how to go further.

6. anonymous

^ yeah :( thank you though!

7. Loser66

oh, I find out y =2x works for all the case since if we replace y =2x, the first term and the second term cancel out 4x^2 -2(x)(2x) =4x^2 -4x^2 =0 while the last term is always a perfect square since 49 y^2 = (7y)^2 Hence for all couple (x,2x) we have a square satisfy the condition.