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A right triangle has legs that are consecutive integers. The hypotenuse is two greater than the shortest let. Use a quadratic equation to find the dimensions of the right triangle.
Solution
when you say hypotenuse, it means you have a right triangle
h^2 = L^2 + S^2 and h=2+S and L=S+1
(2+S)^2 = (S+1)^2 + S^2
It’s 5-4-3 triangle
S^2 + 4S + 4 = S^2 + 2S + 1 + S^2
S^2 -2S – 3 = 0
(S-3)(S+1) 0
S=3
L=4
h = 5
ignore S=-1, unless you enjoy an alternative universe of negative space and time
S=-1
L=0
h=1, which is maybe a degenerate “triangle” maybe like the vector from the origin to the point (0,-1) mathematically it does seem to be a 2nd solution. It’s sort of like the Twilight Zone, a place beyond sight & sound, or “Flatland” as Prof. Sheldon Cooper might call it, only this is not 2 dimensional land, it’s worse: 1 dimensional land. Maybe inside a Black hole that devours most everything. A triangle with one negative side, one zero side and a hypotenuse of real positive length. Not something you see every day.