Question 946035
{{{x}}}= length of the shortest leg in meters.
Then,
{{{2x+6}}}= length of the hypotenuse in meters.
Applying the Pythagorean theorem,
{{{x^2+24^2=(2x+6)^2}}}
{{{x^2+576=4x^2+24x+36}}}
{{{0=4x^2-x^2+24x+36-576}}}
{{{0=3x^2+24x-540}}}
Dividing both sides of the equal sign by 3, we get
{{{0=x^2+8x-180}}}
Factoring , we get
{{{0=(x+18)(x-10)}}} ---> {{{system {{({x=10,"or",x=-18)}}}
Since {{{x}}} , the length of the shortest leg in meters, cannot be a negative number,
the length of the shorter leg is {{{highlight(10meters)}}}.