Question

if two rectangles have the same perimeter, will they always be congruent? yes no

Explanation:

Step1: Recall perimeter formula

Perimeter of rectangle: \( P = 2(l + w) \), where \( l \) is length, \( w \) is width.

Step2: Give counterexample

Take rectangle 1: \( l = 5 \), \( w = 3 \). Perimeter: \( 2(5 + 3) = 16 \).
Rectangle 2: \( l = 6 \), \( w = 2 \). Perimeter: \( 2(6 + 2) = 16 \).
These have same perimeter but different side lengths, so not congruent.

Answer:

No