# Calculate the width and height of a rectangle, given its diagonal and area

Here's my problem: "In a rectangle, the diagonal is 6 and area 14. The perimeter is: a) 10 b) 14 c) 16 d) 18 e) 20.

So I know that $x^2 + y^2 = 36$, and that $xy = 14$, but I'm having problems figuring out what the width and height equals.. (sorry if anything's unclear, English is not my primary language , but I can't find any information on this in my own language).

Hint: try to use $(x+y)^2=x^2+y^2+2xy$
• you have all the information to compute what $(x+y)^2$ is. Therefore you can compute $x+y$, and deduce the perimeter. You don't need to find out what $x$ and $y$ are, knowing $x+y$ is enough. – Denis Aug 3 '14 at 13:38