# 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).

## 1 Answer

Hint: try to use $(x+y)^2=x^2+y^2+2xy$

• I'm sorry, but my brain can't wrap around this problem. I already used an online calculator to find out it was 16, but I still don't understand this (and that's because I'm a kid that has not experienced these kind of math problems before). To explain futher, I don't know where I should use (x+y)^2, I know that it'll give me the squared width + squared height + 2*width*height, and I don't know why and how I use this. – didnotcomeuptosomething Aug 3 '14 at 10:20
• 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
• (x+y)^2 = 36 + 28 = 64 Square of 64 = 8. 8 = x+y. Therefore the perimeter is 16. So as you can see I finally figured it out, and I have to really thank you for that. I forgot that I already knew what y^2 + x^2 was, and that I already had 2xy, my brain really wasn't up for math today. Once again, thank you for reminding me what I forgot :) – didnotcomeuptosomething Aug 3 '14 at 16:35