Represent the following problem 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. - Wired Faculty

Question

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Represent the following problem situations in the form of quadratic equations:
The area of a rectangular plot is 528 m². 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.

Solution

Let breadth of the rectangle = x m Then, length of the rectangle = (2x + 1) m
∵ Area of the rectangle = (2x + 1) x m²
According to the given condition,
(2x + 1)x = 528 ⇒ 2x² + x – 528 = 0
which is a quadratic equation in x.
Solving this equation by factorisation method, we get

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rightwards double arrow

straight x left parenthesis 2 straight x plus 33 right parenthesis minus 16 left parenthesis 2 straight x plus 33 right parenthesis equals 0

rightwards double arrow

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rightwards double arrow

2 straight x plus 33 equals 0 space space or space space straight x space minus space 16 space equals space 0

rightwards double arrow

space space straight x equals fraction numerator negative 33 over denominator 2 end fraction space space or space space straight x space equals space 16

But breadth cannot be -ve.
∴ x = 16
Hence, breadth of the rectangle = 16 m and length of the rectangle = 2 x 16 + 1 = 33 m.

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Quadratic Equations

Represent the following problem situations in the form of quadratic equations:
The area of a rectangular plot is 528 m². 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.

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:
x²– 2x = (–2) (3 – x)

Check whether the following are quadratic equations:
(x – 2) (x + 1) = (x – 1) (x + 3)

Check whether the following are quadratic equations:
(x – 3) (2x + 1) = x(x + 5)

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:
x² + 3x + 1 = (x – 2)²

Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem 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.

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NCERT Sample Papers

Entrance Exams Preparation

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Quadratic Equations

Represent the following problem situations in the form of quadratic equations:The area of a rectangular plot is 528 m2. 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.

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:x2 – 2x = (–2) (3 – x)

Check whether the following are quadratic equations:(x – 2) (x + 1) = (x – 1) (x + 3)

Check whether the following are quadratic equations:(x – 3) (2x + 1) = x(x + 5)

Check whether the following are quadratic equations:(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:x2 + 3x + 1 = (x – 2)2

Check whether the following are quadratic equations:(x + 2)3 = 2x(x2 – 1)

Check whether the following are quadratic equations:x3 – 4x2 – x + 1 = (x – 2)3.

Represent the following problem situations in the form of quadratic equations:The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem 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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Represent the following problem situations in the form of quadratic equations:
The area of a rectangular plot is 528 m². 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.

Check whether the following are quadratic equations:
x²– 2x = (–2) (3 – x)

Check whether the following are quadratic equations:
(x – 2) (x + 1) = (x – 1) (x + 3)

Check whether the following are quadratic equations:
(x – 3) (2x + 1) = x(x + 5)

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:
x² + 3x + 1 = (x – 2)²

Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem 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.