Question

the perimeters of two similar triangles are in 4 is to 9 ratio then ratio of the corresponding sides is ​

Answer 1

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→ Answer :

The ratio of the perimeters of two similar triangles = the ratio of their corresponding sides

$=>\frac{4}{9}$  is ratio of corresponding sides

→ Step-by-step explanation :

If $\triangle$ ABC ~  $\triangle$ XYZ  

$\frac{AB}{XY}=\frac{BC}{YZ} =\frac{AC}{XZ}$ = k ( corresponding sides of similar triangles)

$=> AB = K* XY .... (1)$

$BC = K * YZ...(2)$

$AC = K * XZ ... (3)$

By adding (1), (2), & (3)

$AB + BC + AC = K ( XY + YZ + XZ)\\\\=>(\frac{AB + BC + AC}{XY + YZ + XZ} ) = K$

$=>(\frac{Perimeter*of*ABC}{perimeter*of*XYZ} )= \frac{AB}{XY} =\frac{BC}{YZ} =\frac{AC}{XZ}$

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