Question 1014409
.
C=L=length of ladder; A=height up side of building=L-2;
B=distance from building to bottom of ladder=L-4
.
{{{A^2+B^2=C^2}}}
{{{(L-2)^2+(L-4)^2=L^2}}}
{{{(L^2-4L+4)+(L^2-8L+16)=L^2}}}
{{{2L^2-12L+20=L^2}}}
{{{L^2-12L+20=0}}}
{{{(L-2)(L-10)=0}}}
{{{L-2=0}}} {{{OR}}} {{{L-10=0}}}
{{{L=2}}} {{{OR}}} {{{L=10}}}
Since L must be greater than 4 (Distance from building is L-4), 
L=10.
.
ANSWER: Length of ladder is 10 feet.
.
CHECK:
C=L=10 feet
A=L-2=10-2=8 feet
B=L-4=10-4=6 feet
.
{{{A^2+B^2=C^2}}}
{{{8^2+6^2=10^2}}}
{{{64+36=100}}}
{{{100=100}}}