Question 43532
leg = a
other leg = b
{{{a + b + 25 = 56}}}
{{{a + b = 31}}}
{{{b = 31 - a}}}
Next:
{{{a^2 + b^2 = c^2}}}
{{{a^2 + b^2 = 625}}}
Plug:
{{{a^2 + (31 - a)^2 = 625}}}
{{{a^2 + 961 - 62a + a^2 = 625}}}
{{{2a^2 - 62a + 336 = 0}}}
{{{a^2 - 31a + 168 = 0}}}
{{{(a - 24)(a - 7) = 0}}}
{{{a = 24}}} and {{{a = 7}}}
Plug:
{{{b = 31 - a}}}
{{{b = 31 - 24}}} and {{{b = 31 - 7}}}
{{{b = 7}}} and {{{b = 24}}}
The leg's lengths: 7m and 24m