Question

describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 9 feet, 16 feet

Answer 1

7 ≤ x ≤ 25

Explanation:

Triangle Inequality Theorem

The sum of any two sides of a triangle is greater than or equal to the third side:

• a + b ≥ c

Therefore, the longest side of the triangle is "c".

Let the longest side be "x":

• a = 9
• b = 16

Therefore:

• 9 + 16 ≥ x
• 25 ≥ x

Let the longest side be 16:

• a = 9
• c = 16

Therefore:

• 9 + x ≥ 16
• x ≥ 7

As 9 < 16, the longest side cannot be 9.

Therefore, the length of the third side of the triangle, given that the other two sides are 9 ft and 16 ft is greater than or equal to 7, and less than or equal to 25:

• 7 ≤ x ≤ 25