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The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

  • A.8
  • B.12
  • C.6
  • D.2

Answer: D

Let the sides of the rectangle be l and b respectively.

From the given data, 

(√l⊃2; + b⊃2;) = (1 + 108 1/3 %)lb 

=> l⊃2; + b⊃2; = (1 + 325/3 * 1/100)lb

= (1 + 13/12)lb

= 25/12 lb

=> (l2 + b⊃2;)/lb = 25/12 

12(l2 + b⊃2;) = 25lb 

Adding 24lb on both sides 

12l2 + 12b⊃2; + 24lb = 49lb 

12(l2 + b⊃2; + 2lb) = 49lb 

but 2(l + b) = 28 => l + b = 14 

12(l + b)⊃2; = 49lb 

=> 12(14)⊃2; = 49lb 

=> lb = 48 

Since l + b = 14, l = 8 and b = 6 

l - b = 8 - 6 = 2m.

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