SOLUTION: A field has a rectangular shape. If the area is 5 square meters and the perimeter is 24 meters how far is it from one corner to the opposite corner? I tried making a list of len

Question 347798: A field has a rectangular shape. If the area is 5 square meters and the perimeter is 24 meters how far is it from one corner to the opposite corner?
I tried making a list of lengths and widths to get a perimeter of 24 but then the area was never 5 and if I found sides with an area of 5 the perimeter was no longer 24. I know I need to use the pythagorean theorem to find the diagonal but I don't know how to find the sides first.
Thanks.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
area = 5 sq.m
perimeter = 24
..
l*b= 5
l= 5/b
2(l+b)=24
l+b=12
plug value of l
5/b +b=12
5+b^2/ b =12
(5+b^2) =12b
b^2-12b+5 =0
solve the equation using quadratic formula
you will get
length =11.57
width = 0.43
CHECK
11.57*0.43= 4.98
find diagonal
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