Question 954664
c=hypotenuse; a=shortest leg=c-12cm; b=longer leg=c-6cm
{{{a^2+b^2=c^2}}} Substitute for a and b.
{{{(c-12cm)^2+(c-6cm)^2=c^2}}}
{{{(c^2-24c+144)+(c^2-12c+36)=c^2}}}
{{{2c^2-36c+180=c^2}}} Subtract {{{c^2}}} from each side.
{{{c^2-36c+180=0}}}*[invoke quadratic "c", 1, -36, 180 ]
Possible solutions are 30 and 6 Since a=c-12, 6 doesn't work.
c=30 cm
ANSWER 1: The hypotenuse is 30 cm.
a=c-12cm=30-12cm=18cm
ANSWER 2: The shortest leg is 18 cm.
b=c-6cm=30-6cm=24cm
ANSWER 3: The longer leg is 24 cm.
CHECK:
{{{a^2+b^2=c^2}}}
{{{18^2cm^2+24^2cm^2=30^2cm^2}}}
{{{324cm^2+576cm^2=900cm^2}}}
{{{900cm^2=900cm^2}}}