How can I find the legs of a right triangle using only the hypotenuse length, 600, and the fact that all the sides have to add up to 1400?

Answer 1

Let x and y be the sides.

By Pythagorean Theorem, x^2 + y^2 = 600^2.
x+y+600 = 1400

Answer 2

a + b + c = 1400
a + b + 600 = 1400
a + b = 800

using Pythagorean theorem
a^2 + b^2 = 600^2

a + b = 800
a^2 + b^2 = 600^2

solve simultaneously
I got
a = 258.579
b = 541.421

or
a = 541.421
b = 258.579