Answer:
The Perimeter of similar triangles are ALWAYS in same ratio as the corresponding sides.
Step-by-step explanation:
Triangle is a polygon.
The perimeter of Polygon is sum of all the sides.
⇒Perimeter of Triangle is sum of all three sides.
Let say, we have two similar triangles whose sides are in s :1
Also let sides of a triangle are x, y, & z
then the sides of other triangle are given by : s.x, s.y and s.z
Now, we find the perimeter of triangles
perimeter of first triangle, P = x + x + z
Perimeter of second triangle, P' = s.x + s.y + s.z
⇒ P' = s × (x+ y+ z)
⇒ P' = s × P
⇒[tex]\frac{P'}{P}=\frac{s}{1}[/tex]
∴ The perimeter of similar triangles are always in the same ratio as the corresponding sides.
Thus, The Perimeter of similar triangles are ALWAYS in same ratio as the corresponding sides.
