The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of

Hi,
the method explained above is the correct method..
But another method which you could use is the POE..

now the perimeter of rectangle is 20+25+20+25=90..
so perimeter of rhombus has to be less than 90.. elimiate E..

Also perimeter of the rhombus has to be greater than 20+20+20+20=80, as the side of rhombus is the hypotenuse , which has to be more than the side of the same triangle, 20
eliminate A..

lets see the remaining choices..
A rhombus has all equal sides, so each side = perimeter/4
B. 82 yards... side= 20.5
C. 84 yards..side=21
D. 85 yards..side=21.25

now this side = hypotenuse osf a right angle triangle whose one side is 20..
lets see if hyp=20.5 and one side = 20, what is the second side...
\(\sqrt{20.5^2-20^2}\)=\(\sqrt{(20.5-20)(20.5+20)}\)
...\(\sqrt{.5*40.5}\)=\(\sqrt{.5*.5*81}\)=4.5..

this exactly fits in as other side of rhombus..
25=4.5=20.5..