Question

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.

Answer 1

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.

: )

Answer 2

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.