SOLUTION: An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2(squared). Find the dimensions of the garden.

Algebra ->  Equations -> SOLUTION: An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2(squared). Find the dimensions of the garden.      Log On


   

Question 467901: An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2(squared). Find the dimensions of the garden.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the garden = W m
Let the length of the garden = L m
given:
(1) +W%2AL+=+5000+ m2
(2) +2W+%2B+2L+=+300+ m
---------------------
(2) +W+%2B+L+=+150+
and
(1) +L+=+5000%2FW+
so, by substitution:
(2) +W+%2B+5000%2FW+=+150+
(2) +W%5E2+%2B+5000+=+150W+
(2) +W%5E2+-+150W+%2B+5000+=+0+
Use quadratic formula:
W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-150+
+c+=+5000+
W+=+%28-%28-150%29+%2B-+sqrt%28+%28-150%29%5E2-4%2A1%2A5000+%29%29%2F%282%2A1%29+
W+=+%28+150+%2B-+sqrt%28+22500+-+20000+%29%29%2F2+
W+=+%28+150+%2B-+sqrt%28+2500+%29%29%2F2+
W+=+%28+150+%2B-+50%29%2F2+
+W+=+75+%2B+25+
+W+=+100+
and
+W+=+75+-+25+
+W+=+50+
and
(2) +W+%2B+L+=+150+
(2) +50+%2B+100+=+150+
The dimensions are 50 x 100 m2
check:
(1) +W%2AL+=+5000+ m2
(1) +50%2A100+=+5000+
(1) +5000+=+5000+
OK