SOLUTION: a rectangle has a perimeter of 22 and an area of 30. What is the length of the rectangle's diagonal?

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Question 306475: a rectangle has a perimeter of 22 and an area of 30. What is the length of the rectangle's diagonal?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
xy=30
x=30/y
2x+2y=22
2(30/y)+2y=22
60/y+2y=22
(60+2y*y)/y=22
60+2y^2=22y
2y^2-11y+60=0
2(y^2-y+30)=0
2(y-6)(y-5)=0
y-6=0
y=6 ans.
x*6=30
x=30/6
x=5 ans
y-5=0
y=5 ans.
x*5=30
x=30/5
x=6 ans.
Proof:
2*5+286=22
10+12=22
22=22
The diagonal:
5^2+6^2=c^2
25+36=c^2
61=c^2
c=sqrt61
c=7.81 ans. for the diagonal.