Question 3 Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^2 ? If so, find its length and breadth.
Class 10 - Math - Quadratic Equations Page 91
Answers
Answered by
3
Let the breadth of mango grove be l.
Length of mango grove will be 2l.
Area of mango grove = (2l) (l)= 2l2
2l2 = 800
l2 = 800/2 = 400
l2 - 400 =0
Comparing this equation with al2 + bl + c = 0, we get
a = 1, b = 0, c = 400
Discriminant = b2 - 4ac
= (0)2 - 4 × (1) × ( - 400) = 1600
Here, b2 - 4ac > 0
Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.
l = ±20
However, length cannot be negative.
Therefore, breadth of mango grove = 20 m
Length of mango grove = 2 × 20 = 40 m
Length of mango grove will be 2l.
Area of mango grove = (2l) (l)= 2l2
2l2 = 800
l2 = 800/2 = 400
l2 - 400 =0
Comparing this equation with al2 + bl + c = 0, we get
a = 1, b = 0, c = 400
Discriminant = b2 - 4ac
= (0)2 - 4 × (1) × ( - 400) = 1600
Here, b2 - 4ac > 0
Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.
l = ±20
However, length cannot be negative.
Therefore, breadth of mango grove = 20 m
Length of mango grove = 2 × 20 = 40 m
Answered by
2
For a quadratic equation ax² + bx + c =0, the term b² - 4ac is called discriminant (D) of the quadratic equation because it determines whether the quadratic equation has real roots or not ( nature of roots).
D= b² - 4ac
So a quadratic equation ax² + bx + c =0, has
i) Two distinct real roots, if b² - 4ac >0 , then x= -b/2a + √D/2a &x= -b/2a - √D/2a
ii) Two equal real roots, if b² - 4ac = 0 , then x= -b/2a or -b/2a
iii) No real roots, if b² - 4ac <0
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Solution:
Let breadth of a rectangular mango grove is =x m
Length of a rectangular mangrove = 2x m (given)
A.T.Q
Area of rectangular mangrove = 800 m ² (given)
Area of rectangular mangrove = length × breadth
800 = 2x × x
2x² = 800
x² =800/2
x² =400
x² - 400
on comparing with ax² + bx + c =0,
a =1 , b= 0, c= -400
Discriminant = b² – 4ac
= (0)2 – 4 × (1) × ( – 400) = 1600
D =1600
Here, b2 – 4ac > 0
Two distinct real roots, if b² - 4ac >0 , then x= -b/2a + √D/2a &x= -b/2a - √D/2a
x= -b/2a + √D/2a
x= 0 / 2×1 + √1600/ 2×1
x = 40/2= 20x= 20
x= -b/2a - √D/2a
x= 0 / 2×1 - √1600/ 2×1
x = - 40/2= -20
Since negative sign is not possible because breadth never be negative
Hence ,breadth of mango grove(x) = 20 m
Length of mango grove(2x) = 2 × 20 = 40 m
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Hope this will help you.....
D= b² - 4ac
So a quadratic equation ax² + bx + c =0, has
i) Two distinct real roots, if b² - 4ac >0 , then x= -b/2a + √D/2a &x= -b/2a - √D/2a
ii) Two equal real roots, if b² - 4ac = 0 , then x= -b/2a or -b/2a
iii) No real roots, if b² - 4ac <0
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Solution:
Let breadth of a rectangular mango grove is =x m
Length of a rectangular mangrove = 2x m (given)
A.T.Q
Area of rectangular mangrove = 800 m ² (given)
Area of rectangular mangrove = length × breadth
800 = 2x × x
2x² = 800
x² =800/2
x² =400
x² - 400
on comparing with ax² + bx + c =0,
a =1 , b= 0, c= -400
Discriminant = b² – 4ac
= (0)2 – 4 × (1) × ( – 400) = 1600
D =1600
Here, b2 – 4ac > 0
Two distinct real roots, if b² - 4ac >0 , then x= -b/2a + √D/2a &x= -b/2a - √D/2a
x= -b/2a + √D/2a
x= 0 / 2×1 + √1600/ 2×1
x = 40/2= 20x= 20
x= -b/2a - √D/2a
x= 0 / 2×1 - √1600/ 2×1
x = - 40/2= -20
Since negative sign is not possible because breadth never be negative
Hence ,breadth of mango grove(x) = 20 m
Length of mango grove(2x) = 2 × 20 = 40 m
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Hope this will help you.....
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