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Question

A man of height y is standing between two buildings with heights x and z respectively as shown in the figure. Then, which of the following statements is true about the relation of the heights?

A
x=y=z
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B
1x=1y=1z
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C
1x=1y+1z
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D
1x+1z=1y
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Solution

The correct option is D 1x+1z=1y
Given, QBAC,PAAC and RCAC.
In ΔAPC and ΔBQC,
ACP=BCQ [common]
PAC=QBC [each 90]
ΔAPCΔBQC [by AA similarity]
APBQ=ACBCxy=ACBC...(i)
Now, in ΔARC and ΔAQB,
ACR=ABQ [each 90]
CAR=BAQ [common]
ΔARCΔAQB [by AA similarity]
RCQB=ACAB
zy=ACAB...(ii)
From Eqs. (i), we get
BC=yxAC ...(iii)
From Eq. (ii), we get
AB=yzAC
Adding Eqs. (iii) and (iv), we get
AB+BC=(yx+yz)ACAC=y(1x+1z)AC1y=1x+1z

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