Question 965851
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c=hypotenuse; a=shorter leg=c-10cm; b=longer leg=c-5cm
{{{a^2+b^2=c^2}}}
{{{(c-10cm)^2+(c-5cm)^2=c^2}}}
{{{(c^2-20c+100cm)+(c^2-10c+25)=c^2}}} Subtract c^2 from each side.
{{{c^2-30C+125=0}}}
{{{(c-5)(c-25)=0}}}
{{{c-5=0}}} {{{or}}} {{{c-25=0}}}
{{{c=5}}} {{{or}}} {{{c=25}}}
ANSWER 1: The hypotenuse is 25 centimeters.
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a=c-10cm=25cm-10cm=15 cm
ANSWER 2: The shorter leg is 15 centimeters.
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b=c-5cm=25cm-5cm=20 cm
ANSWER 3: The longer leg is 20 centimeters.
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CHECK:
{{{a^2+b^2=c^2}}}
{{{(15cm)^2+(20cm)^2=(25cm)^2}}}
{{{225cm^2+400cm^2=625cm^2}}}
{{{625cm^2=625cm^2}}}