Question 1101135
<br>With the given information, the length of BC is 12.<br>
Consider triangles ADB, BDC, and CDA.<br>
The area of triangle ADB is {{{(1/2)(5)(x)}}}
The area of triangle BDC is {{{(1/2)(12)(z)}}}
The area of triangle CDA is {{{(1/2)(13)(y)}}}<br>
The area of triangle ABC is the sum of the areas of those three triangles:<br>
{{{(5x/2)+(12z/2)+(13y/2) = 30}}}
{{{(5x+12z+13y)/2 = 30}}}
{{{5x+13y+12z = 60}}}<br>