Question

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of the triangle are 13 feet and 23 feet. Find the possible lengths of the third side.

Answer 1

Answer:

Between the lengths of 10 and 36 (exclusive).

Step-by-step explanation:

Since the lengths of any two sides is always greater than the third, the shortest possible length of the third side must be greater than 23 when added to 13. 23-13 = 10, so the third side must be greater than 10.

However, the third side also cannot exceed the length of the sum of the other two sides. 23+13 = 36, therefore the length must be less than 36.

The possible lengths of the third side lie between 10 and 36 (exclusive).

If we use 'l' for length, this range can be represented as follows:

$10 < l < 36$

Hope this helped!