Reprsent the following situations in the form of quadratic equations :
The area of a rectangular plot is 528 m^{2}. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
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Reprsent the following situations in the form of quadratic equations :
The area of a rectangular plot is 528 m^{2}. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Reprsent the following situations in the form of quadratic equations :
The area of a rectangular plot is 528 m^{2}. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
Reprsent the following situations in the form of quadratic equations :
The product of two consecutive positive integers is 306. We need to find the integers.
Reprsent the following situations in the form of quadratic equations :
The product of two consecutive positive integers is 306. We need to find the integers.
Let one positive integer be x’.
The Next integer is (x + 1)
Their product is 306.
∴ x (x + 1) = 306
x^{2} + x = 306
∴ x^{2} + x – 306= 0.
This is required equation.
Now, we have to solve for positive integer.
x^{2} + x – 306 = 0
x^{2} + 18x – 17x – 306 = 0
x(x + 18) – 17(x + 18) = 0
(x + 18) (x – 17) = 0
If x + 18 = 0, then x = -18
If x – 17 = 0, then x = 17
∴ x = 18, OR x = 17.
Reprsent the following situations in the form of quadratic equations :
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Reprsent the following situations in the form of quadratic equations :
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
Let the present age of Rohan be ‘x’, then His mother’s age will be (x + 26)
After 3 years, Age of Rohan is (x + 3).
After 3 years his mother’s age will be
= (x + 26 + 3) = (x + 29)
Then product of their ages is 360.
∴ (x + 3) (x + 29) = 360
x^{2} + 29x + 3x + 87 = 360
x^{2} + 32x + 87 = 360
x^{2} + 32x + 87 – 360 = 0
x^{2} + 32x – 273 = 0.
This is required equation.
Now, we have to solve for the value of ‘x’:
x^{2} + 32x – 273 = 0
x^{2} + 39x – 7x – 273 = 0
x(x + 39) – 7(x + 39) = 0
(x + 39) (x – 6) = 0
If x + 39 = 0, then x = -39
If x – 6 = 0, then x = 7
Present age of Rohan’s mother
= x + 26
= 7 + 26 = 33 years.
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.
2x^{2} + x = 528
∴ 2x^{2} + x – 528 = 0 is the required equation.
Now, we have to find out the value of ‘x’ :
2x^{2} + x – 528 = 0
2x^{2} – 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.