Question 896676
hypotenuse is 20.


one of the sides is x.
the other side is (x+4)


pythagorus says:


x^2 + (x+4)^2 = 20^2 which becomes:


x^2 + x^2 + 8x + 16 = 400


subtract 400 from both sides of the equation and combine like terms to get:


2x^2 + 8x - 384 = 0


divide both sides of the equation by 2 to get:


x^2 + 4x - 192 = 0


factor to get:


(x + 16) * (x - 12) = 0


solve for x to get:


x = -16 or x = 12


x can't be negative so the solution is x = 12


if x = 12, then x+4 = 16


your sides are 12 and 16.


by pythagorus, 12^2 + 16^2 = 20^2 which becomes:


144 + 256 = 400 which becomes:


400 = 400 confirming the solution is good.


the sides are 12 and 16 and the hypotenuse is 20


this triangle is similar to a 3/4/5 triangle since 12/16/20 is a multiple of 3/4/5 by a factor of 4.


the triangles have the same angles and the sides are proportional which is the definition of similar triangles.


you didn't need to know that.


it's an extra.


your solution is that the sides are 12 and 16.