What conditions must hold for a right triangle with legs x and y to have its perimeter numerically equal to its area?

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Answer 1 · 2017-11-28T16:21:08

Condition is #xy+8=4x+4y#

Area of right angled triangle whose legsare#x# and #y# is#1/2xy#

and its perimeter is #x+y+sqrt(x^2+y^2)#

if #x+y+sqrt(x^2+y^2)=1/2xy#

or #sqrt(x^2+y^2)=(xy)/2-(x+y)=(xy-2x-2y)/2#

or #x^2+y^2=1/4(4x^2+4y^2+x^2y^2+8xy-4x^2y-4xy^2)#

or #4x^2+4y^2=4x^2+4y^2+x^2y^2+8xy-4x^2y-4xy^2#

or #x^2y^2+8xy=4x^2y+4xy^2#

and dividing by #xy# as it is non-zero, we get

#xy+8=4x+4y#