Which of the following cannot be the sides of a triangle
a. 3 cm, 4 cm, 5 cm
b. 2 cm, 4 cm, 6 cm
c. 2.5 cm, 3.5 cm, 4.5 cm
d. 2.3 cm, 6.4 cm, 5.2 cm

Solution:

We have to determine which of the given options cannot be the sides of a triangle.

We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

(i) considering 3 cm, 4 cm, 5 cm

Let the two sides be 3cm and 4cm

Let the third side be 5 cm

Now, sum of two sides = 3 + 4 = 7 cm

So, 7 > 5

Therefore, option a can be the sides of a triangle.

(ii) considering 2 cm, 4 cm, 6 cm

Let the two sides be 2cm and 4cm

Let the third side be 6 cm

Now, sum of two sides = 2 + 4 = 6 cm

So, 6 = 6

Therefore, option b cannot be the sides of a triangle.

(iii) considering 2.5 cm, 3.5 cm, 4.5 cm

Let the two sides be 2.5 cm and 3.5 cm

Let the third side be 4.5 cm

Now, sum of two sides = 2.5 + 3.5 = 6 cm

So, 6 > 4.5

Therefore, option c can be the sides of a triangle.

(iv) considering 2.3 cm, 6.4 cm, 5.2 cm

Let the two sides be 2.3 cm and 6.4 cm

Let the third side be 5.2 cm

Now, sum of two sides = 2.3 + 6.4 = 8.7 cm

So, 8.7 > 5.2

Therefore, option d can be the sides of a triangle.

✦ Try This: Can 3 cm, 5 cm, 7 cm be the sides of a triangle. Justify your answer

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Sample Problem 3

Which of the following cannot be the sides of a triangle? a. 3 cm, 4 cm, 5 cm, b. 2 cm, 4 cm, 6 cm, c. 2.5 cm, 3.5 cm, 4.5 cm, d. 2.3 cm, 6.4 cm, 5.2 cm

Summary:

2 cm, 4 cm, 6 cm cannot be the sides of a triangle

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