SOLUTION: A 548 m fence surrounds a rectangular field. The diagonal distance from corner to corner is 194 m. Find the area of the rectangular field.

Question 861747: A 548 m fence surrounds a rectangular field. The diagonal distance from corner to corner is 194 m. Find the area of the rectangular field.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
length = l
width = w
2(l+w)=548
l+w= 274................(1)
the diagonal and the sides form a right triangle
apply Pythagoras theorem
l^2+w^2=194^2
(l+w)^2-2lw=194^2
plug l+w
274^2-2lw=194^2
2lw= 274^2-194^2
2lw=37440
lw= 37440/2
lw= 18720
l=18720/w
l+w = 274
w+ 18720/w= 274
w^2+18720=274w
w^2-274w+18720=0
w^2-144w-130w+18720=0
w(w-144)-130(w-144)=0
(w-144)(w-130)=0
w= 144 OR 130
Dimensions are 144 m by 133m

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