The foot of a ladder is 2m away from a vertical wall. the height of the top of the ladder is half a meter less than the length of the ladder. find the length of the ladder.
you

So use pythagorean theorem
a^2+b^2=c^2
a=base
b=height
c=legnth of ladder

a=2
b=c-0.5
subsitute
2^2+(c-0.5)^2=c^2
4+c^2-c+0.25=c^2
add like terms
c^2-c+4.25=c^2
subtract c^2 from both sides
-c+4.25=0
add c to both sides
4.25=c

the legnth of the ladder is 4.25 m