Problema Solution
A ladder is leaning against a building . The distance from the bottom of the ladder to the building is 9th less than the length of the ladder. How high up the side of thee building is the top of the ladder if that distance is 2ft less than the length of the ladder?
Answer provided by our tutors
Let length of ladder be l.
Let distance of bottom of ladder to wall be x.
Let the distance between botton of wall and where ladder touches the wall be y.
x=l-9
y=l-2
Acc to pythagoras theorem,
l2=x2+y2
l2=(l-9)2+(l-2)2
l2=l2+81-18l+l2+4-4l
0=85-22l+l2
l2-22l+85=0
l2-5l-17l+85=0
l(l-5)-17(l-5)=0
l=17 or l=5
l=5 is not possible as xxannot be less than 0.
Hence, l=17,
therefore y=17-2=15 ft high is the top of the ladder from teh building.