Answer / jagdeep

two poles of 5m and 7m respetively. a wire is tied from top
of one to bottom of other. at what heightthe two wires will
cross

We will use algebra and an x-y coordinate axis to solve this
problem. Let the pole of 5 m be located at the origin, so
the two ends of that pole are at (0,0) and (0,5). Let the
pole of 7 m be located on the x-axis at a distance of a to
the right of the first pole, so the two ends of that pole
are at (a, 0) and (a,7). The problem does not state the
distance between the poles, so we let that equal an unknown
constant "a" for now. We will find out later that the value
of "a" is irrelevant.

So we want to draw two lines, one from the base of one to
the top of the other and vice versa.

Line 1: Points (0,0) and (a,7)
Slope of line 1: m = 7/a
Intercept of line 1: b = 0
Equation of line 1: y = (7/a) x

Line 2: Points (0,5) and (a,0)
Slope of line 2: m=-5/a
Intercept of line 2: b = 5
Equation of line 2: y = (-5/a)x + 5

The point where these lines meet is the place where the
wires cross!

Solve equation 1 for x:
x = (a/7) y
Substitute this into equation 2:
y = (-5/a) (a/7) y + 5
Notice that a cancels out!
y = (-5/7)y + 5
(12/7) y = 5
12y = 35
y = 35/12 = 2.912

Answer / rohit_allinterview

Can be calculated using similarity properties of triangles.
Steps:
Step1: Treat line AB as pole1 of 5mts.
Step2: Treat line CD as pole2 of 7mts.
Step3: Let E be the intersection of AD and BC.
Step4: Drop E perpendicular to BD at F. EF=? to b calculated
Step5: Trngl EFD and Trng ABD are similar, Hence
AB/EF= BD/FD. ==> 5/EF=BD/FD

So, EF = 5*FD/BD ------> Eq.1

Similarily, considering trngl's CDB, EFB. They are similar.
Hence, CD/EF = BD/BF ===> 7/EF= BD/(BD-FD)

So, EF = 7*(BD-FD)/BD ----> Eq .2

Solve eq 1 and eq 2. i.e., Equate eq 1 and eq 2.

Hence u get 12*FD=7*BD => FD=7*BD/12 -----> Eq 3

Solve Eq 1 and Eq 3. i.e., substitute FD in Eq1.
EF=35/12= 2.916


Plz rate it if it is correct/incorrect. For any
clarification mail me at rohit_vit2020@yahoo.co.in

Answer / kiran

actually we can calcuate base by applying pythagoras thm.
but finding intersection pt. is bit tricky so rohit if u can
clarify your answer post here

Answer / madhu

I think without knowing the distance b/w the two poles, we
cant find intersecting point height.

Answer / karthik

No rope from top of one pole can reach bottom of other..
so we could't calculate the intersection point from ground

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