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Answer:
Step-by-step explanation:
Let ‘x’ and ‘y’ be the length & breadth of the vegetable garden
GIVEN : Area of vegetable garden = 100 m²
Area of rectangle = Length x breadth
x x y = 100
x = 100/y…………….(1)
For fencing We calculate the perimeter.
Here, the fencing will be on three sides of the vegetable garden because one side of the vegetable garden will act as the compound wall.
Given - Perimeter of 3 sides of the vegetable garden= 30 m
x + x + y = 30
2 x + y = 30
2(100/y) + y = 30
[From eq 1]
(200/y) + y = 30
(200 + y²)/y = 30
200 + y² = 30 y
y² - 30 y + 200 = 0
y² - 10 y – 20 y + 200 = 0
[By middle term splitting
y (y – 10) - 20 (y – 10) = 0
(y – 10) (y – 20) = 0
y – 10 = 0 or y – 20 = 0
y = 10 or y = 20
Put these values of y in eq 1,
x = 100/y
If y = 10
x =100/10
x = 10 m
If y = 20
x = 100/20
x = 5 m
Hence, the required dimensions are (10 m ,10 m) or (20 m , 5 m).
Answer:
Step-by-step explanation:
Let ‘x’ and ‘y’ be the length & breadth of the vegetable garden
GIVEN : Area of vegetable garden = 100 m²
Area of rectangle = Length x breadth
x x y = 100
x = 100/y…………….(1)
For fencing We calculate the perimeter.
Here, the fencing will be on three sides of the vegetable garden because one side of the vegetable garden will act as the compound wall.
Given - Perimeter of 3 sides of the vegetable garden= 30 m
x + x + y = 30
2 x + y = 30
2(100/y) + y = 30
[From eq 1]
(200/y) + y = 30
(200 + y²)/y = 30
200 + y² = 30 y
y² - 30 y + 200 = 0
y² - 10 y – 20 y + 200 = 0
[By middle term splitting
y (y – 10) - 20 (y – 10) = 0
(y – 10) (y – 20) = 0
y – 10 = 0 or y – 20 = 0
y = 10 or y = 20
Put these values of y in eq 1,
x = 100/y
If y = 10
x =100/10
x = 10 m
If y = 20
x = 100/20
x = 5 m
Hence, the required dimensions are (10 m ,10 m) or (20 m , 5 m).