Question

It is possible to have a triangle with the following sides? (I) 3cm,4cm and 5cm (ii) 6cm,6cm and 6cm (iii) 4cm,4cm and 8cm (iv) 3cm,5cm and 7cm​

Answer 1

Answer:

only 4th one is not possible

first three are possible

Answer 2

Required Answer:

$\dag$ 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 = 3cm
• b = 4cm
• c = 5cm

Now, 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 cm

In 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 = 6cm
• b = 6cm
• c = 6cm

Now, 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 cm

In 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 cm

Sides :–

• a = 4cm
• b = 4cm
• c = 8cm

Now, 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 cm

In 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 cm
• b = 5 cm
• c = 7 cm

Now, 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 cm

In 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.