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