NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 Question 2 (i)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 2 (i)

Question:

Represent the following 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.

Given:

Area of rectangular plot = 528 m2

Length = 1 + 2 × Breadth

To Find:

Quadratic equation representing the situation to find the length and breadth of the plot.

Formula:

WKT, Area of a rectangle = Length × Breadth.

Solution:

Let the breadth of the rectangular plot (in metres) = x

According to the given condition, the length is one more (+) than twice (2x) its breadth.

⇒ Length (in metres) = 2x + 1
WKT, Area = Length × Breadth

⇒ 528 = (2x + 1) × x

⇒ 528 = 2x2 + x
Rearrange the equation into the standard quadratic form ax2 + bx + c = 0:

⇒ 2x2 + x - 528 = 0

Result:

The situation can be represented by the quadratic equation:
2x2 + x - 528 = 0.
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