How many right triangles have a hypotenuse that measures 8x+1 meters and legs that measure 8x−1 meters and x+6 meters? what are the dimension

A²+b²=c²

c=8x+1
a=8x-1
b=x+6

(8x-1)²+(x+6)²=(8x+1)²
64x²-16x+1+x²+12x+36=64x²+16x+1
65x²-4x+37=64x²+16x+1
minus (64x²+16x-1) from both sides
x^2-20x+36=0
factor
what 2 numbers multiply to 36 and add to -20
-18 and -2
(x-18)(x-2)=0
set to zero
x-18=0
x=18

x-2=0
x=2

there are 2 positive solutions, therefor 2 right triangles
their dimentinos can be found by subsitution

for x=18
hyptonuse 145m, legs are 143m and 24m

for x=2
hypotonuse is 17m, legs are 15m and 8m