Question

2. Represent the following situations in the form of quadratic equations:
(1) 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.​

Answer 1

Answer:

Q. 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.​

Sol,

Let the breadth of the rectangle be x m

The length of the rectangle is (2x+1) m

As per question,

Area = 528 m^2

Length X Breadth = 528

x (2x+1) = 528

2x^2 +x -528 = 0

2x^2 + 33x - 32x - 528 = 0

2x(x+33)-32(x+33)=0

(2x-32) (x+33)=0

(2x-32)=0 and (x+33)=0

2x = 32 and x= -33

x = 16,

Here,

x= -33 is an extraneous value

Therefore,

x = 16

Breadth = 16 m

Length = 2x+1

= 2 X 16+1

= 33 m

Thanks for asking.

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Answer 2

Answer:

Let us consider,

Breadth of the rectangular plot = x m

Thus, the length of the plot = (2x + 1) m.

As we know,

Area of rectangle = length × breadth = 528 m^2

Putting the value of length and breadth of the plot in the formula, we get,

(2x + 1) × x = 528

⇒ 2x^2 + x =528

⇒ 2x^2 + x – 528 = 0

Therefore,

the length and breadth of plot,

satisfies the quadratic equation, 2x^2 + x – 528

= 0,

which is the required representation of the problem mathematically.