Question 1190352

given:

{{{CD = 3x+10}}} 
{{{AB = 2x+15}}} 
{{{AD = 7x+25 }}}
{{{BC = 24}}}


The segment addition theorem tells you that


 {{{ AB +BC +CD = AD}}}.........substitute given values

{{{2x+15+24+3x+10=7x+25}}}........solve for {{{x}}}

{{{5x+49=7x+25}}}

{{{49-25=7x-5x}}}

{{{24=2x}}}

{{{x=12}}}


the length of {{{CD}}} is:

{{{CD = 3*12+10}}}

{{{CD = 46}}}