Question

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!

Answer 1

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 ?

Answer 2

yeah its -2xy :((

Answer 3

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

Answer 4

ohh, okay2 thanks! :)

Answer 5

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

Answer 6

^ yeah :( thank you though!

Answer 7

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.