the perimeter of rectangular garden is 60 metres. If the length of garden is increase by 2 metres and breadth decrease by 2 metres, the area of garden becomes 24square metres less. solving the equation by graph, find the length and breadth of rectangular garden
Answer:
Length = 20 m, Breadth = 10m
Step-by-step explanation:
Let the length be x
Let the breadth be y
Original area = xy
New length = x + 2
New breadth = y – 2
New area = [tex](x+2)(y-2) = xy – 2x +2y – 4[/tex]
Perimeter = 2(x+y) = 60 m
x+y = 30 m —- (i)
By problem,
[tex]xy-2x+2y-4 = xy – 24\\2x – 2y= 20\\x-y = 10 — (ii)[/tex]
Solving i and ii
[tex]x-y = 10\\x+y = 30\\\\x= 20 m\\y = 10 m[/tex]
Length = 20 m
Breadth = 10m
CHECK –
Length = 20m
Breadth = 10 m
Perimeter = 2(20+10) m = 2 X 30 = 60 m
Original area = 20 X 10 = 200 m²
New length =22 m
New breadth = 8 m
New area = 176 m²
Now,
200-176 = 24 m²