Question

The perimeters of similar triangles are in the same ratio as the corresponding sides.

Always
Sometimes
Never

Answer 1

A. Always is the Answer to this

Answer 2

The perimeters of similar triangles are always in the same ratio as the corresponding sides.

Explanation:

The perimeter of triangle is sum of all the sides of the triangle.

Let we have two similar triangles with a scale factor s

Therefore, if sides of one triangle are a,b, and c

then the sides of the second triangle are given by : as, bs, and cs

Now, perimeter of first triangle, P = a + b + c

Perimeter of second triangle, Q = sa + sb + sc

⇒ Q = s × (a+ b+ c)

⇒ Q = s × P

Hence, The perimeters of similar triangles are always in the same ratio as the corresponding sides.

Therefore, the correct answer is ALWAYS