What will be the Area of the Rectangle? If

If the diagonal of a rectangle is 17 cm long and the perimeter of the rectangle is 46 cm, then the area of the rectangle is:

  1. 120 cm2
  2. 112 cm2
  3. 132 cm2
  4. 289 cm2
Harsh Vardhan Professor Asked on 29th July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1)  120 cm2
    Explanation:-
    Let the length of a rectangle = X m   &   width of the rectangle = Y m.
    Formula-
    Perimeter of a rectangle = 2 (l + b)
    Where, l = length of the rectangle   &    b = breadth of the rectangle

    Then, 2 (X + Y )  = 46
    X + Y = 46/2
    X + Y = 23

    Formula-
    diagonal of the rectangle =  X2 + Y 2
    Where, X & Y are the length & breadth of the rectangle.

    Then, X2 + Y2 = 172  = 289
    Now, (X + Y )2 = 232
    X2 + Y2 + 2 X Y = 529
    289 + 2 X Y = 529
    2 X Y = 529 – 289
    X Y = 240/2
    X Y = 120
    The area of the rectangle = X Y = 120 cm2
    Hence, the answer is (1) 120 cm2

    Anurag Mishra Professor Answered on 29th July 2015.
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