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General

Easy

Question

# A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side.

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
- while finding possible lengths of third side use below formula
- difference of two side < third side < sum of two sides

## The correct answer is: Hence, all numbers between 4 and 26 will be the length of third side.

### Step-by-step explanation:

Given:

In triangle, sides are 11 inches and 15 inches.

a = 11 inches, b = 15 inches.

Step 1:

Find length of third side.

According to triangle inequality theorem,

c < a + b

∴ c < 11 + 15

c < 26

Step 2:

difference of two side < third side < sum of two sides

b – a < c < a + b

15 – 11 < c < 11 + 15

4 < c < 26

Hence, all numbers between 4 and 26 will be the length of third side.

Final Answer:

Hence, all numbers between 4 and 26 will be the length of third side.

Step 2:

difference of two side < third side < sum of two sides

Hence, all numbers between 4 and 26 will be the length of third side.

Final Answer:

Hence, all numbers between 4 and 26 will be the length of third side.

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