Question 1005015
Step 1: Define a variable
{{{x}}}= length of the shorter leg, in meters.


Step 2: Express other measurements based on the variable defined above.
{{{x+8}}}= length of the shorter leg, in meters.
{{{2x-8}}}= length of the hypotenuse/


Step 3: Apply the Pythagorean theorem
{{{(2x-8)^2=x^2+(x+8)^2}}}


Step 4: Work on the above equation (simplify and solve)
{{{(2x-8)^2=x^2+(x+8)^2}}}
{{{(2x)^2+2(2x)(-8)+8^2=x^2+x^2+2(x)(8)+8^2}}}
{{{4x^2-32x+8^2=x^2+x^2+16x+8^2}}}
{{{4x^2-32x=2x^2+16x}}}
{{{4x^2-32x-2x^2-16x=0}}}
{{{2x^2-48x=0}}}
{{{2x(x-24)=0}}}--->{{{x=24}}} is the only solution that makes sense, because
{{{x=0}}} does not make sense.


Step 5: Find the other lengths
{{{x+8=24+8=32}}} and {{{2x-8=2*24*8=48-8=40}}} .


Step 6: Answer in words, with units if that is what is expected.
The shorter leg measures {{{highlight(24meters)}}} .
The longer leg measures {{{highlight(32meters)}}} .
The hypotenuse measures {{{highlight(40meters)}}} .