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!

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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!

Mathematics
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  • 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 ?
yeah its -2xy :((
  • 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 \[ 4\sqrt{4x^2-2xy +49y^2} \]

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ohh, okay2 thanks! :)
if x =1, y =2 we have the expression = 14^2 , but not sure how to go further.
^ yeah :( thank you though!
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.

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