SOLUTION: The perimeter of a rose garden is 140m and the area is 1200m squared. find the length and width of the garden.

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rose garden is 140m and the area is 1200m squared. find the length and width of the garden.      Log On


   

Question 575365: The perimeter of a rose garden is 140m and the area is 1200m squared. find the length and width of the garden.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+2W+%2B+2L+
+A+=+W%2AL+
given:
+P+=+140+ m
+A+=+1200+ m2
---------------
(1) +140+=+2W+%2B+2L+
(2) +1200+=+W%2AL+
------------------
(2) +W+=+1200%2FL+
Substitute (2) into (1)
(1) +140+=+2%2A%28+1200%2FL+%29+%2B+2L+
Multiply both sides by +L+
(1) +140L+=+2400+%2B+2L%5E2+
(1) +2L%5E2+-+140L+%2B+2400+
(1) +L%5E2+-+70L+%2B+1200+
Use quadratic equation
L+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-70+
+c+=+1200+
L+=+%28-%28-70%29+%2B-+sqrt%28+%28-70%29%5E2-4%2A1%2A1200+%29%29%2F%282%2A1%29+
L+=+%28+70+%2B-+sqrt%28+4900+-+4800+%29%29+%2F+2+
L+=+%28+70+%2B-+sqrt%28+100++%29%29+%2F+2+
+L+=+%28+70+%2B+10+%29+%2F+2+
+L+=+40+
and
(2) +W+=+1200%2FL+
(2) +W+=+1200%2F40+
(2) +W+=+30+
The length is 40 m
The width is 30 m