Question

ction B (2 Marks
RECTANGULAR FIELD
Rahul is a farmer who has a rectangular plot. He has to plough his farm. But he does not know
the length and breadth of his farm. Will you help Rahul?
The area of his farm is given by polynomial P(x) =(x2-7x+12) square units.
Area=P(x)=x2-7x+12
26. Give possible expressions for length and breadth.
27. Find the perimeter of rectangular plot.
(2 marks)
(2 marks)​

Answer 1

Answer:

Area = 12m2

Perimeter = 14m

Step-by-step explanation:

Area = x2 - 7x + 12

We will solve this quadratic equation by splitting the middle term

x2 - 7x + 12

= x2 - 4x -3x + 12  [ sum of -4x and -3x is 7x; product of -4 and -3 is 12] we found out 4 and 3 because 4 * 3 = 12

Taking x as common we get:

x( x - 4) -3(x - 4)

(x-3) (x-4)  [ we wrote x - 4 once here and we are left with x - 3 so we wrote it separately]

now to make x-3 = 0 so value of x = 3

similarly x-4 = 0 so values of x = 4

we have two values ie 3 and 4

4 is our length[because it is greater] and 3 is our breadth

Area of a rectangle = length * breadth

Area = 4 * 3 = 12 m2

Perimeter = 2(Length + Breadth)

Perimeter = 2(4+3)

Perimeter = 2(7)

Perimeter = 14 m

Answer 2

Answer:  Length of rectangular plot= x - 4 units

               Breadth of rectangular plot= x - 3 units

               Perimeter of rectangular plot= (4x - 14) units.

Step-by-step explanation:

(i) A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles.

Let's us take the length of the rectangular plot to be 'l' units and the breadth to be 'b' units. Then, we can write:

l= length of the rectangle.

b= breadth of the rectangle.

P(x) = l × b = (x² - 7x + 12)

By factorizing the given polynomial, we get:

P(x) = (x - 4)(x - 3)

Therefore, the length and breadth are:

length = x - 4 units and

breadth = x - 3 units

or

length = x - 3 units and breadth = x - 4 units

(ii)  Perimeter of Rectangle could be considered as one of the important formulae of the rectangle.

The perimeter of the rectangular plot is:

2(l + b) units

Putting the values of l and b from part (i), we get:

2[(x - 4) + (x - 3)] units

= 2(2x - 7) units

= 4x - 14 units

The perimeter of the rectangular plot is (4x - 14) units.

To learn more about Area of Rectangle from the given link:

https://brainly.in/question/51399722

To learn more about Perimeter of Rectangle from the given link:

https://brainly.in/question/23508466

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