Δ ABC & Δ DEF are similar triangles, where segment AB and segment DE are corresponding sides. If DE
= 2 AB and perimeter of Δ ABC is 20, what is the perimeter of Δ DEF?

The correct answer is: 40

Hint:-
Perimeter of a triangle = sum of all sides
Properties of similar triangles-
Corresponding angles are equal.
Length of Corresponding sides are in the same proporsion.
Step-by-step solution:-
Δ ABC & Δ DEF are similar triangles, where AB and DE are corresponding sides.
∴ AB ~ DE, BC ~ EF & AC ~ DF
DE = 2 AB --------------- (Given)
∴ = --------------- (Equation i)
We know that the proportion of length of all corresponding sides of similar triangles are equal.
∴ = = = ---------- (From Equation i) -------- (Equation ii)
Let AB = x, BC = y & AC = z
∴ DE = 2x, EF = 2y & DF = 2z ----------- (From Equation ii)
Now,
Perimeter of Δ ABC = 20 --------- (Given)
∴ AB + BC + AC = 20
∴ x + y + z = 20 ---------- (Equation iii)
Perimeter of Δ DEF = DE + EF + DF
∴ Perimeter of Δ DEF = 2x + 2y + 2z
∴ Perimeter of Δ DEF = 2 (x + y + z)
∴ Perimeter of Δ DEF = 2 (20) ------------- (From Equation iii)
∴ Perimeter of Δ DEF = 40 units
Final Answer:-
  Option B i.e. 40 is the correct Option.