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Hi Manas

Here X and Y are not equal. It's kind of tough to explain a geometry problem without diagram, still let me try. You must be aware that in a right angle triangle

(Height)^2 + (_base_)^2 = (Hypotenuse)^2

Suppose here if Height = H & _base_ = B and Hyp. = C

Then originaly; H^2 + B^2 = C^2

Now if H has become = (H-X) and B has become (B+Y)
The new equation has to be:

(H-X) ^2 + (B+Y)^2 = C^2 = H^2 +B^2

(H^2 + X^2 - 2HX) + (B^2+Y^2 + 2 BY) = H^2 + B^2
X^2 +Y^2 = 2 (HX-BY)

So we can not conclude X=Y.

To make it more clear lets consider a Right angle triangle with sides (6, 8 , 10)
If I decrease 6 by 1 and increase 8 by 1 the new equation will become

(6-1)^2+ (8+1)^2 = 25+84 = 109 which is not equal to 6^2 + 8^2 = 100.

Hope this makes you more comfortable...........

Feel free to shoot back