Question 1056237
{{{drawing(200,100,-1,17,-1,8,
locate(6,0,a),locate(12.17,2.85,b), locate(5,3.5,c),
triangle(0,0,12,0,12,5) )}}}
`
The shortest leg of a triangle is 7 centimeters shorter 
than the other leg
<pre><b>
{{{drawing(200,100,-1,17,-1,8,
locate(6,0,a),locate(12.17,2.85,b=a-7), locate(3.8,4,c=13),
triangle(0,0,12,0,12,5) )}}}

{{{a^2+b^2=c^2}}}
{{{a^2+(a-7)^2=13^2}}}
{{{a^2+(a^2-14a+49)=169}}}
{{{a^2+a^2-14a+49=169}}}
{{{2a^2-14a-120=0}}}
{{{a^2-7a-60=0}}}
{{{(a-12)(a+5)=0}}}
a-12 = 0;   a+5 = 0
   a = 12;    a = -5

Discard the negative answer.

Since b=a-7,
      b=12-7,
      b=5 

{{{drawing(200,100,-1,17,-1,8,
locate(6,0,12),locate(12.17,2.9,5), locate(5,3.6,13),
triangle(0,0,12,0,12,5) )}}}

Edwin</pre></b>