Question

In the xy plane there are three given points A(0;0) B(x;0) C(0;y) which form a right triangle whose perimeter and area are both equal to 30 .Find the sum x+y.

Answer 1

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Answer 2

Distance between AB =
$\sqrt{ {(x)}^{2} + {0}^{2} } = x$
Similarly Distance between AC =
$y$
Distance between BC =
$\sqrt{ {x}^{2} + {y}^{2} }$

we know
(Area)
$\frac{1}{2} \times y \times x = 30 = xy = 60$
(perimeter)
$x + y = 30 - \sqrt{ {x}^{2} + {y}^{2} }$
$x + y = 30 - \sqrt{ {(x + y)}^{2} - 2xy}$
let , k = x+y
$k = 30 - \sqrt{ {k}^{2} - 120}$
K= 17

X+Y = 17