A cubical box has a side-length of 1m. It is placed next to a wall which is perpendicular to the ground. A ladder 4.9 meters long is placed so that it rests against the ground, the and an edge of the box as shown in the diagram.

Question

A cubical box has a side-length of 1m.  It is placed next to a wall which is perpendicular to the ground.  A ladder 4.9 meters long is placed so that it rests against the ground, the and an edge of the box as shown in the diagram.

anonymous · Answer

Let xm and ym be the lengths of AB and AC respectively
a. find BD in tems of x
b. find CF in terms of y
c. prove that  /\ DBE is similar to /\ FEC. Hence show that xy=x+y
d. prove that x2 + y2=24
e. use parts c and d to prove that (y+y)2 - 2(x+y)-24=0
f. at what height does the ladder rest against the wall?
g. does f have more than one solution?

pfenn1 · Answer

Okay.  a. find BD in terms of x
AD + BD = AB right?

pfenn1 · Answer

Okay.  We know what AD and AB are from what the problem gives us, right?

pfenn1 · Answer

So write the equation for BD in terms of x?

pfenn1 · Answer

yes

pfenn1 · Answer

no, not necessarily....we don't know what BD is at this point.
AB  = AD + BD =1 + BD = xm rearrange and solve for BD
BD=xm-1

pfenn1 · Answer

would what be 7 meters?

pfenn1 · Answer

I don't know how you are getting these numbers?  Can you show me your work?

pfenn1 · Answer

Oh.  Yeah, I was a little thrown by that as well. I don't think we can use those boxes, because the box  is 1 m but 9 of the little boxes, so what does that mean?  So I am ignoring them for now.

pfenn1 · Answer

a. they only seem to want the length of BD in terms of x so what is that?

pfenn1 · Answer

I think you might be getting ahead of yourself. They just want you to find BD and CF in terms of x and y for now.

pfenn1 · Answer

I showed you above that for a. BD = xm - 1, remember?

pfenn1 · Answer

I don't know yet.  The first question is
Let xm and ym be the lengths of AB and AC respectively 
a. find BD in tems of x
BD = xm - 1

the second question is
b. find CF in terms of y
Can you do this one?

pfenn1 · Answer

I could.  I have already shown you.
AC = AF + CF =1 + CF = ym 
rearrange and solve for CF 
CF=ym-1

anonymous · Answer

I know there are comments from another person but can anyone explain it in a better way to where i can understand it easier?

anonymous · Answer

|dw:1336774065283:dw|
so you have the expression for DB and FC, and FE=DE=1
put in the values and solve to prove xy=x+y