Question 189631
Let x=length of the longer leg
hypotenuse=10 feet
shorter leg = 2x-10

Pythagorean theorem:

{{{10^2=x^2+(2x-10)^2}}}
{{{100=x^2+(4x^2-40x+100)}}}
{{{100=5x^2-40x+100}}}

Subtracting 100 from both sides, we get:

{{{0=5x^2-40x}}}

Dividing both sides by 5x we get:

{{{0=x-8}}}

Adding 8 on both sides we get:

{{{x=8}}}

Shorter Leg = 2x-10 = 2*8-10=6 feet