A rectangle has a length 3 m more than its width and a perimeter numerically equal in value to its area. The integral part of the value of its diagonal is:

Given:
The perimeter of the rectangle = The area of a rectangle.
Formula used:
Diagonal = $$\sqrt{{length}^2 + {breadth}^2}$$​​

Solution:
Let the breadth of the rectangle = x
So the length of rectangle = x + 3
According to the given conditions;
Perimeter = Area
=> Perimeter of the rectangle = 2(length + breadth)
=> Area of the rectangle = (length × breadth)
=> 2(x + 3 + x) = (x + 3) × x
=> 2x + 6 + 2x = x² + 3x
=> x² - x - 6 = 0
=> x² - 3x + 2x - 6 = 0
=> x(x - 3) + 2(x - 3) = 0
=> (x - 3) × (x + 2) = 0
=> x = 3 and x = (-2)
So, x = 3 then Length = 6
Diagonal = $$\sqrt{{length}^2 + {breadth}^2}$$​

=> Diagonal = $$\sqrt{6^2 + 3^2}$$​​
=> Diagonal = $$\sqrt{45}$$​​

=> Diagonal = 6.708
Hence, the integral part of the diagonal is;
= 6. ​​