Question

if the perimeter of two similar triangles are in ratio 1:3. the ratio of corresponding sides is​

Answer 1

Step-by-step explanation:

Yes ! The ratio of the perimeters of two similar triangles = the ratio of their corresponding sides. It can be proved.

If Triangle ABC ~ Triangle XYZ

AB/XY = BC/YZ = 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)

=>( AB + BC + AC)/(XY + YZ + XZ) = K

=> (Perimeter of tri ABC)/(perimeter of tri XYZ) = AB/XY = BC/YZ = AC/XZ