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Q2(i):
Represent the following situations in the form of quadratic equations : (i) 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.
Solution :
Given:
1. The shape of the plot is rectangular.
2. The area of the rectangular plot ($A$) = $528$ $m^2$.
3. The relationship between length ($l$) and breadth ($b$): The length is one more than twice its breadth.
To Find:
Represent the given situation in the form of a quadratic equation.
Step 1: Defining the Variables
Let the breadth of the rectangular plot be $x$ metres.
According to the problem, the length is one more than twice the breadth.
Therefore, the length of the plot $l = (2x + 1)$ metres.
Step 2: Applying the Formula for Area
The area of a rectangle is given by the formula:
$Area = Length \times Breadth$
$A = l \times b$
Step 3: Formulating the Equation
Substitute the given values and the expressions defined in Step 1 into the area formula:
$528 = (2x + 1) \times x$
Step 4: Simplifying the Expression
Distribute $x$ into the parentheses:
$528 = 2x^2 + x$
Step 5: Rearranging into Standard Quadratic Form
The standard form of a quadratic equation is $ax^2 + bx + c = 0$.
Subtract $528$ from both sides of the equation:
$2x^2 + x - 528 = 0$
Justification:
The equation $2x^2 + x - 528 = 0$ is a quadratic equation because it is a polynomial equation of degree 2, where $a = 2$, $b = 1$, and $c = -528$.
Final Answer: The quadratic equation representing the situation is $2x^2 + x - 528 = 0$, where $x$ represents the breadth of the plot in metres.
More Questions from Class 10 Mathematics Quadratic Equations EXERCISE 4.1
- Q1(i): Check whether the following are quadratic equations : (i) $(x + 1)^2 = 2(x – 3)$
- Q1(ii): Check whether the following are quadratic equations : (ii) $x^2 – 2x = (–2)(3 – x)$
- Q1(iii): Check whether the following are quadratic equations : (iii) $(x – 2)(x + 1) = (x – 1)(x + 3)$
- Q1(iv): Check whether the following are quadratic equations : (iv) $(x – 3)(2x +1) = x(x + 5)$
- Q1(v): Check whether the following are quadratic equations : (v) $(2x – 1)(x – 3) = (x + 5)(x – 1)$
- Q1(vi): Check whether the following are quadratic equations : (vi) $x^2 + 3x + 1 = (x – 2)^2$
- Q1(vii): Check whether the following are quadratic equations : (vii) $(x + 2)^3 = 2x (x^2 – 1)$
- Q1(viii): Check whether the following are quadratic equations : (viii) $x^3 – 4x^2 – x + 1 = (x – 2)^3$
- Q2(ii): Represent the following situations in the form of quadratic equations : (ii) The product of two consecutive positive integers is $306$. We need to find the integers.
- Q2(iii): Represent the following situations in the form of quadratic equations : (iii) 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.
- Q2(iv): Represent the following situations in the form of quadratic equations : (iv) A train travels a distance of $480$ km at a uniform speed. If the speed had been $8$ km/h less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.
CBSE Solutions for Class 10 Mathematics Quadratic Equations
Chapters in CBSE - Class 10 Mathematics
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