Question

The area of a rectangle is 21 cm square .if one exceed the other by 4 cm find the dimension of the rectangle

Answer 1

Let the breadth be x.....

Then,

length = x + 4.....

Also, Area = length * breadth...


So, x(x + 4) = 21

x^2 + 4x - 21 = 0

(x + 7)(x - 3) = 0

So,

x is 3 cm..... { Remember length is not -ve }..


Hence,

Breadth = 3cm...

Length = 3 + 4 = 7cm

Answer 2

Answer :
_________

Length = 7 cm and

Breadth = 3 cm.

SOLUTION :
_________

Given that : The area of rectangle = 21 cm²

Also given that the one is exceed the other by 4

Let, Breadth = x cm

then, Length will be (x+4) cm

As we know that : Area of rectangle = l×b

According to the question :

$x \times (x + 4) = 21 \\ \\ = > {x}^{2} + 4x = 21 \\ \\ = > {x}^{2} + 4x - 21 = 0 \\ \\ = > {x}^{2} + 7x - 3x - 21 = 0 \\ \\ = > x(x + 7) - 3(x + 7) = 0 \\ \\ = > (x + 7)(x - 3) = 0$

Required value of x = –7 and 3

The value of x = –7 doesn't exist.

So, the value of x = breadth = 3 cm.

Now, Length will be : x+4 = 3+4 = 7 cm.