Question

Which of the following does not represent the lengths of the sides of a triangle?

2 cm , 6 cm , 7 cm
5 cm , 2 cm , 5 cm
3 cm , 10 cm , 15 cm​

Answer 1

Option (3): 3 cm, 10 cm, 15 cm does not represent the lengths of the sides of a triangle.

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Let's understand a few concepts:

To choose the correct option we need to know one basic rule of triangle i.e., the Triangle Inequality Theorem.

$\boxed{\underline{\bold{Triangle\:Inequality\:Theorem}}}:$

The sum of the lengths of any two sides of a triangle should always be greater than the length of the 3rd side.

If a, b and c are the 3 sides of a triangle then:

a + b > c

b + c > a

a + c > b

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Let's solve the given problem:

Checking for 2 cm , 6 cm , 7 cm:

2 + 6 = 8 > 7

6 + 7 = 13 > 2

2 + 7 = 9 > 6

∴ 2 cm, 6 cm and 7 cm does represent the lengths of sides of a triangle.

Checking for 5 cm , 2 cm , 5 cm:

5 + 2 = 7 > 5

5 + 5 = 10 > 2

∴ 5 cm, 2 cm and 5 cm does represent the lengths of sides of a triangle.

Checking for 3 cm , 10 cm , 15 cm:

3 + 10 = 13 < 15

10 + 15 = 25 > 3

3 + 15 = 18 > 10

∴ 3 cm, 10 cm and 15 cm does not represent the lengths of sides of a triangle.

Thus, option(3): 3 cm, 10 cm and 15 cm does not represent the lengths of sides of a triangle.

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Answer 2

Answer:

The side length 3 cm , 10 cm , 15 cm​ doesn't represents the sides of triangle.

Step-by-step explanation:

For this we use triangle inequality theorem.

What is triangle inequality theorem?

The triangle inequality theorem states that the sum of length of two sides of a triangle is always greater than the third side of triangle.

For side 2 cm , 6 cm , 7 cm

2+6>7

6+7>2

2+7>6

So, triangle is possible.

For side length 5 cm , 2 cm , 5 cm.

5+2>5

5+5>2

So, triangle is possible.

For side length 3 cm , 10 cm , 15 cm​.

3+10<15  i.e; sum of length of two sides is smaller than the length of third side so triangle is not possible.

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