Square PQRS side 20 cm – Four triangles by joining opposite vertices:\nBy joining opposite vertices (i.e., both diagonals), the square is partitioned into four congruent triangles. Find the sum of the perimeters of the four triangles.

Introduction / Context:
Both diagonals of a square meet at the centre, creating 4 congruent isosceles triangles each with sides: two radii (half-diagonals) and one side of the square.

Given Data:

• Square side s = 20 ⇒ diagonal = s√2 = 20√2 ⇒ half-diagonal (radius to vertex) = 10√2.

Concept / Approach:
Each triangle (centre with two adjacent vertices) has sides 10√2, 10√2, and 20 ⇒ perimeter per triangle = 20 + 20√2. Sum of four = 4(20 + 20√2) = 80 + 80√2.

Final Answer:
80√2 + 80