The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. Formulate the quadratic equation to determine the length and breadth of the plot.
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Answered by
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Step-by-step explanation:
Let the breadth of rectangular plot (b) be ’x’ m. Then the length of th plot is one more than twice its breadth,
∴ Length (l)= 2x + 1 m.
But Length × Breadth = Area of rectangle
l × b = A
∴ x × (2x + 1) = 528 sq.m.
2x2 + x = 528
∴ 2x2 + x – 528 = 0 is the required equation.
Now, we have to find out the value of ‘x’ :
2x2 + x – 528 = 0 2x2 – 32x + 33x – 528 = 0
2x(x – 16) + 33(x – 16) = 0 (x – 16) (2x + 33) = 0
If x – 16 = 0,
then x = 16 If 2x + 33 = 0, then x = -33/2
∴ Breadth (b) = 16 m.
Length (l) = (2x + 1) = 2(16) + 1 = 32 + 1 = 33m
∴ Length (l) = 33 m
Breadth (b) = 16 m
Answered by
5
Answer:
Step-by-step explanation:
Let the breadth of rectangular plot (b) be ’x’ m. Then the length of th plot is one more than twice its breadth,
∴ Length (l)= 2x + 1 m.
But Length × Breadth = Area of rectangle
l × b = A
∴ x × (2x + 1) = 528 sq.m.
2x2 + x = 528
∴ 2x2 + x – 528 = 0 is the required equation.
Now, we have to find out the value of ‘x’ :
2x2 + x – 528 = 0 2x2 – 32x + 33x – 528 = 0
2x(x – 16) + 33(x – 16) = 0 (x – 16) (2x + 33) = 0
If x – 16 = 0,
then x = 16 If 2x + 33 = 0, then x = -33/2
∴ Breadth (b) = 16 m.
Length (l) = (2x + 1) = 2(16) + 1 = 32 + 1 = 33m
∴ Length (l) = 33 m
Breadth (b) = 16 m
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