d Answer: The sides of option (i) , (ii) and (iv) can form a triangle.★ Sides of options (iii) can't form a triangle._________________________Tip:• A triangle can be formed only when sum of two sides of a triangle is greater than the third side.Procedure:• Here, by applying the above law to check whether it is possible to have a triangle with the GIVEN sides or not. Solution:(i) 3cm,4cm and 5cm ✔Sides :–a = 3cmb = 4cmc = 5cmNow, as we KNOW that : A triangle can be formed only when sum of two sides of a triangle is greater than the third side.Thus,• a + b > c→ 3 cm + 4 cm > 5 cm→ 7 cm > 5 cm• a + c > b→ 3 cm + 5 cm > 4 cm→ 8 cm > 5 cm• b + c > a→ 4 cm + 5 cm > 3 cm→ 9 cm > 5 cmIn all cases , third side is smaller than the sum of two remain sides. Thus, a triangle having sides of 3cm,4cm and 5cm can form a triangle.(ii) 6cm,6cm and 6cm ✔Sides :–a = 6cmb = 6cmc = 6cmNow, as we know that : A triangle can be formed only when sum of two sides of a triangle is greater than the third side.Thus,• a + b > c→ 6 cm + 6 cm > 6 cm→ 12 cm > 6 cm• a + c > b→ 6 cm + 6 cm > 6 cm→ 12 cm > 6 cm• b + c > a→ 6 cm + 6 cm > 6 cm→ 12 cm > 6 cmIn all cases , third side is smaller than the sum of two remain sides. Thus, a triangle having sides of 6cm,6cm and 6cm can form a triangle.(iii) 4 cm , 4 cm , 8 cmSides :–a = 4cmb = 4cmc = 8cmNow, as we know that : A triangle can be formed only when sum of two sides of a triangle is greater than the third side.Thus,• a + b > c→ 4 cm + 4 cm > 8 cm→ 8 cm = 8 cm• a + c > b→ 4 cm + 8 cm > 4 cm→ 12 cm > 4 cm• b + c > a→ 4 cm + 8 cm > 4 cm→ 12 cm > 4 cmIn first cases , third side isn't smaller than the sum of two remain sides. Thus, a triangle having sides of 4cm,4cm and 8cm can't form a triangle.(iv) 3cm,5cm and 7cm ✔Sides :–a = 3 cmb = 5 CMC = 7 cmNow, as we know that : A triangle can be formed only when sum of two sides of a triangle is greater than the third side.Thus,• a + b > c→ 3 cm + 5 cm > 7 cm→ 8 cm > 7 cm• a + c > b→ 3 cm + 7 cm > 5 cm→ 10 cm > 5 cm• b + c > a→ 5 cm + 7 cm > 3 cm→ 12 cm > 3 cmIn all cases , third side is smaller than the sum of two remain sides. Thus, a triangle having sides of 3cm,5cm and 7cm can form a triangle.