Question

Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 12 feet and 18 feet.

I attached the picture too.

Answer 1

6 ft < L₃ < 30 ft

Explanation:

To obtain the answer to the question given above, we must bear in mind that:

The sum of the length of two sides of any triangle is always greater than the 3rd length i.e

L₁ + L₂ > L₃

With the above information in mind, we can obtain the answer to the question given above as follow:

Length 1 (L₁) = 12 feet

Length 2 (L₂) = 18 feet

Length 3 (L₃) =..?

Case 1:

L₁ + L₂ > L₃

12 + 18 > L₃

30 > L₃

L₃ < 30 feet

Case 2:

L₁ + L₃ > L₂

12 + L₃ > 18

Collect like terms

L₃ > 18 – 12

L₃ > 6 feet

Thus,

6 feet < L₃

Combining case 1 and 2,we obtained:

6 ft < L₃ < 30 ft

Therefore, the possible Lenght of the 3rd side is : 6 ft < L₃ < 30 ft