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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