SOLUTION: The measures of two sides are given. Between what two numbers must the third side fall? Given: 9 and 15 (Write an inequality to represent your answer)

Question 1191826: The measures of two sides are given. Between what two numbers must the third side fall?
Given: 9 and 15 (Write an inequality to represent your answer)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.

The third side must be between the numbers 15-9 = 6 and 15+9 = 24 6 < c < 24. ANSWER

Solved.

It follows from the triangle inequalities.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

TRIANGLE INEQUALITY: The length of the longest side of a triangle must be less than the sum of the lengths of the other two sides; otherwise a triangle can't be formed.

(1) If the 9 and 15 are the two shorter sides, the third side must be less than 9+15 = 24 to make a triangle.

(2) If 15 is the longest side and one of the other sides is 9, then the long side is 6 longer than that other side, so the length of the third side must be greater than 6 for the three lengths to make a triangle.

ANSWER: The length of the third side must be greater than 6 and less than 24.

RELATED QUESTIONS
The measures of two sides are given 9 and 15. Between what two numbers must the third... (answered by math_tutor2020)
The measure of two sides of a triangle are given. Between what two numbers must the... (answered by Boreal,Alan3354)
The measure of two sides of a triangle are 8 and 50. Between what two numbers must the... (answered by robertb)
The measures of two sides of a triangle are 22 and 17. Between what two numbers must the... (answered by MathLover1)
Suppose you know that two sides of a triangle are 11 cm and 20 cm. Between what two... (answered by stanbon)
If two sides of a triangle are 10 meters and 23 meters long, then the third side must... (answered by Earlsdon,Alan3354)
The measure of two sides of a triangle are 22 and 17. Between what two numbers must the... (answered by scott8148)
what the range for the measure of the third side given the measures of two sides of 82... (answered by robertb)
for each triangle, two sides are given. What is the third side? 15 ft, 33... (answered by gonzo)