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    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 diagona
    Question

    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:

    A.

    7

    B.

    8

    C.

    6

    D.

    9

    Correct option is C

    Given:
    The perimeter of the rectangle = The area of a rectangle.
    Formula used:
    Diagonal = length2+breadth2\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 = length2+breadth2\sqrt{{length}^2 + {breadth}^2}
    => Diagonal = 62+32\sqrt{6^2 + 3^2}​​
    => Diagonal = 45\sqrt{45}​​
    => Diagonal = 6.708
    Hence, the integral part of the diagonal is;
    = 6. ​​

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