Question

If the area of a rectangle is x^2+x−12, what are its length and breadth?

Answer 1

Answer:

Length = ( x - 3 )

Breadth = ( x + 4 )

Given that ;

Area of the Rectangle = x² + x - 12

Area of the Rectangle = L × B

L × B = x² + x - 12

x² + x - 12

x² + 4x - 3x - 12

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

( x - 3 ) ( x + 4 )

Hence ;

Length = ( x - 3 )

Breadth = ( x + 4 )

Proof :

Area of the Rectangle = L × B

( x - 3 ) ( x + 4 )

x² - 12 + 4x - 3x

Area = x² + x - 12

Answer 2

Solution : Here, we know through the question, area of rectangle is x² + x - 12.

Let, area of rectangle is f(x) = x² + x - 12 ----{1}

Now,

➜ f(x) = x² + x - 12

➜ f(x) = x² + 4x - 3x - 12

➜ f(x) = x (x + 4) - 3 (x + 4)

➜ f(x) = (x + 4) (x - 3)

Hence, length of rectangle is (x + 4) and breadth of rectangle is (x - 3)

Now, take value of x = 1

➜ Length of rectangle = (x + 4)

➜ Length of rectangle = (1 + 4)

➜ Length of rectangle = 5 unit

and

➜ Breadth of rectangle = (x - 3)

➜ Breadth of rectangle = (1 - 3)

➜ Breadth of rectangle = - 2 unit

Here, we know that, the width of a rectangle is neither negative nor zero. Hence value of x ≠ 1

Now, Now, take value of x = 2

➜ Length of rectangle = (x + 4)

➜ Length of rectangle = (2 + 4)

➜ Length of rectangle = 6 unit

and

➜ Breadth of rectangle = (x - 3)

➜ Breadth of rectangle = (2 - 3)

➜ Breadth of rectangle = - 1 unit

Here, we know that, the width of a rectangle is neither negative nor zero. Hence value of x ≠ 2

Now, Now, take value of x = 3

➜ Length of rectangle = (x + 4)

➜ Length of rectangle = (3 + 4)

➜ Length of rectangle = 7 unit

and

➜ Breadth of rectangle = (x - 3)

➜ Breadth of rectangle = (3 - 3)

➜ Breadth of rectangle = 0 unit

Here, we know that, the width of a rectangle is neither negative nor zero. Hence value of x ≠ 3

Now, Now, take value of x = 4

➜ Length of rectangle = (x + 4)

➜ Length of rectangle = (4 + 4)

➜ Length of rectangle = 8 unit

and

➜ Breadth of rectangle = (x - 3)

➜ Breadth of rectangle = (4 - 3)

➜ Breadth of rectangle = 1 unit

We know that, the width of a rectangle is neither negative nor zero. Hence, value of x is 4.

Therefore, we know that, value of x is always greater than 3. { ∴ value of x > 3 }

{ Hence, length of rectangle = 8 unit and breadth of rectangle = 1 unit }