Question

# Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.

5 inches, 12 inches

## The correct answer is: Hence, all numbers between 7 and 17 will be the length of third side.

### Answer:

- Hints:

- 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

- Step-by-step explanation:

- Given:

In triangle, sides are 5 inches and 12 inches.

a = 5 inches, b = 12 inches.

- Step-by-step explanation:

- Given:

In triangle, sides are 5 inches and 12 inches.

a = 5 inches, b = 12 inches.

- Step 1:
- Find length of third side.

According to triangle inequality theorem,

c < a + b

∴ c < 5 + 12

c < 17

- Step 1:
- Find length of third side.

According to triangle inequality theorem,

c < a + b

∴ c < 5 + 12

c < 17

- Step 2:

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

- Step 2:

b – a < c < a + b

12 – 5 < c < 5 + 12

7 < c < 17

Hence, all numbers between 7 and 17 will be the length of third side.

- Final Answer:

Hence, all numbers between 7 and 17 will be the length of third side.

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

- while finding possible lengths of third side use below formula

- Given:

- Given:

- Step 1:
- Find length of third side.

- Step 1:
- Find length of third side.

- Step 2:

- Step 2:

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