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General

Easy

Question

# Is it possible to construct a triangle with the given side lengths? If not, explain why not.

3, 6, 9

Hint:

- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
- b < a + c
- c < a + b

## The correct answer is: No, it is not possible to construct triangle with this sides

- Step-by-step explanation:
- Given:

In triangle, sides are 3 cm, 6 cm and 9 cm.

a = 3, b = 6, and c = 9.

- Step 1:
- First check validity.

According to triangle inequality theorem,

a < b + c,

3 < 6 + 9

3 < 15, True

b < a + c,

6 < 3 + 9,

6 < 12, True

c < a + b,

9 < 3 + 6

9 < 9, false

As sides of triangle does not satisfy triangle inequality theorem.

Hence, triangle cannot be constructed with this sides.

- Final Answer:

No, it is not possible to construct triangle with this sides.

As sides of triangle does not satisfy triangle inequality theorem.

Hence, triangle cannot be constructed with this sides.

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