SOLUTION: A triangular window has two sides that measure 82 centimeters and 67 ​centimeters, respectively. The perimeter of the triangle must not exceed 289 centimeters. What

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Question 1153522:
A triangular window has two sides that measure 82 centimeters and 67

​centimeters, respectively. The perimeter of the triangle must not exceed 289

centimeters. What are the possible values for the length of the third side of
the​ window?

The length of the third side of the window must be

less than or equal to
more than or equal to
more than
less than
cm.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A triangular window has two sides that measure 82 centimeters and 67

​centimeters, respectively. The perimeter of the triangle must not exceed 289

centimeters. What are the possible values for the length of the third side of
the​ window?
----------------
"respectively" serves no purpose.

The length of the third side of the window must be
=============================================
Do NOT enter this. How do you think we could use it?

less than or equal to
more than or equal to
more than
less than
cm.
============================================
The length of the 3rd side must be less than the sum of the other 2 sides, and greater than the difference in lengths of the other 2 sides.


Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

In this problem, there are TWO restrictions on the length of the third side from the upper:


    a)  the length of the third side should be less than the sum of two other sides

            third side < 82 + 67 = 149 cm,       (1)

  and

     b)  the length of the third side should be less or equal the perimeter MINUS the sum of the lengths of the two other sides


             third side <= 289 - (82+67) = 140.   (2)


Of two restrictions (1) and (2), the stronger is (2), so


             third side <= 140 centimeters.


Further, from the triangle inequalities, the third side length must be greater than the difference 

             third side > 82 - 67 = 15.


So, your final ANSWER  is  15 < third side <= 140 centimeters.

Solved.


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