For ΔABC and ΔXYZ, ABC⇔XYZ is a similarity. If AB/4 = BC/6 = AC/3, AC = 3 and XY=5, find YZ and XZ.
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It is given that ,
∆ABC ~ ∆XYZ
AB/4 = BC/6 = AC/3 = k
AB = 4k
BC = 6k ,
AC = 3k ;
XY = 5
i ) AB/XY = BC/YZ
=> 4k/5 = 6k/YZ
YZ = ( 6k × 5 )/4k
YZ = 15/2 = 7.5
ii ) AB/XY = AC/XZ
=> 4k/5 = 3k/XZ
XZ = ( 3k × 5 )/4k
XZ = 3.75
Therefore ,
YZ = 7.5
XZ = 3.75
I hope this helps you.
: )
∆ABC ~ ∆XYZ
AB/4 = BC/6 = AC/3 = k
AB = 4k
BC = 6k ,
AC = 3k ;
XY = 5
i ) AB/XY = BC/YZ
=> 4k/5 = 6k/YZ
YZ = ( 6k × 5 )/4k
YZ = 15/2 = 7.5
ii ) AB/XY = AC/XZ
=> 4k/5 = 3k/XZ
XZ = ( 3k × 5 )/4k
XZ = 3.75
Therefore ,
YZ = 7.5
XZ = 3.75
I hope this helps you.
: )
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Dear student,
Solution:For ΔABC and ΔXYZ, ABC⇔XYZ is a similarity.
for that we can write AB/XY = BC/YZ = CA/ZX = m/1
let us assume that common factor of all proportions are m
Given that
AB/4 = BC/6 = AC/3 = m/1
so, AB = 4m
BC = 6m
AC = 3m
given XY = 5
AB/XY = BC/YZ
4m/5 = 6m/YZ
YZ = 5(6m)/4m
YZ = 30/4
YZ = 7.5
2) BC/YZ = CA/ZX
6m/ 7.5 = 3m/ZX
ZX = XZ = 7.5(3m)/6m
XZ = 3.75
Hope it helps you.
AC = 3 and XY=5, find YZ and XZ.
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