Question 919813


if triangle abc is isosceles, angle {{{b}}} is the vertex angle, {{{ab=20x-2}}},{{{ bc=12x+30}}} and {{{ac=25x}}}, find perimeter of triangle {{{abc}}}

Since the triangle is isosceles, {{{ab= bc}}}}, so:

{{{20x-2=12x+30}}}  solve for {{{x}}}


{{{20x-12x=2+3}}}

{{{8x=5}}}

{{{x=5/8}}}

then

{{{ab=20x-2}}} 
=>{{{ab=20(5/8)-2}}}  
=>{{{ab=5(5/2)-4/2}}}  
=>{{{ab=25/2-4/2 }}}
=>{{{ab=21/2}}} 
=>{{{ab=10.5}}}

{{{bc=12x+30}}} 
=>{{{bc=12(5/8)+30}}} 
=> {{{bc=3*5/2+60/2}}}
=> {{{bc=75/2}}}
=> {{{bc=37.5}}}

and 

{{{ac=25x}}} 
=>  {{{ac=25(5/8)}}} 
=>  {{{ac=125/8}}}
=>  {{{ac= 15.625}}}

 perimeter of triangle {{{abc}}}: 
{{{P=ab+bc+ac}}}

{{{P=10.5+37.5+15.6}}}

{{{P=63.6}}}