Question 973405

since triangles {{{similar}}}, corresponding sides are {{{proportional}}}, so

{{{XZ/PM=YZ/PN}}}

given:
{{{PM=x+5}}}
{{{XZ=30}}}
{{{PN=4x-10}}}
{{{YZ=75}}}

then

{{{30/(x+5)=75/(4x-10)}}}.........cross multiply

{{{30(4x-10)=75(x+5)}}}

{{{120x-300=75x+375}}}

{{{120x-75x=300+375}}}

{{{45x=675}}}

{{{x=675/45}}}

{{{x=15}}}

{{{PM=x+5=15+5=20}}}

{{{PN=4x-10=4*15-10=60-10=50}}}


{{{PM=20}}}
{{{XZ=30}}}
{{{PN=50}}}
{{{YZ=75}}}