3. A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only
30m barbed wire, he fences the sides of the rectangular garden letting his house
compound wall act as the fourth side fence.1.write the perimeter of the garden excluding wall.
2.Find the dimension of the garden.
Answers
Answer:
Step-by-step explanation:
1 . Perimeter of garden excluding wall = 30 m
2 . 2 l + b = 30
b = 30 - 2 l
l × b = 100
l × (30 -2 l) = 100
30 l - 2 l² = 100
2 l² -30 l +100 = 0
l² - 15 l +50 = 0
l² - 10 l - 5 l +50 = 0
l (l - 10) -5 (l -10) =0
(l - 5 ) (l-10) = 0
l = 5 or 10 so
b = 20 or 10 So the dimensions can be 5×20 or 10×10
☯ Let the length of one side be x metres and other side be y metres. Then,
He fences three sides of of Rectanglular garden with 30 m barbed wire.
↬ x + y + x = 30
↬y = 39 - 2x ---eq (1)
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Area of vegetable garden = 100 m²
We know that,
★ Area of Rectangle = l × b
Putting values,
↬xy = 100
✇ Putting value of y from eq (1),
↬ x(30 - 2x) = 100
↬ 30x - 2x² = 100
↬ 15x - x² = 50
↬ x² - 15x + 50 = 0
↬x² - 10x - 5x + 50 = 0
↬ (x - 10)(x - 5) = 0
↬ x = 5 , 10
✇ Putting value of x in eq (1),
When x = 5, we have
↬ y = 30 - 2 × 5
↬ y = 30 - 10
↬y = 20
And,
When x = 10, we have
↬ y = 30 - 2 × 10
↬ y = 30 - 20
↬ y = 10
∴ Hence, The dimensions of vegetable garden are, 50 m × 20 m or, 10 m × 10 m.