The Triangle Inequality and Degenerate Triangles
Read this topicExplanations 5
- The Triangle Inequality states that the sum of any two sides is always greater than the third side. In other words, in any triangle ABCABCABC, we have the following inequalities…
By Jeffery Yu, Moor Xu
- The triangle inequality states that the sum of the lengths of two sides of a triangle is greater than the length of the third side. Equality holds if the triangle is degenerate;…
By Sujay Kazi, Ishwar Karthik, Victor Wang
- The triangle inequality states that, if the sides of a triangle are xxx, yyy, and zzz, then the following: Note: if the inequality was not strict, it would include degenerate tr…
By Ahaan Rungta
- Click here for practise questions of basic level on Triangle Inequality. Hope you get the concept right!
By Devarsh Ruparelia, Moor Xu
- (Videos) Triangle Inequality Theorem by Matka Kranjčević and Mr. K's Flipped Classroom If you have 3 random sides, it is not true that you can always make a triangle. These 3 si…
By Christine, Alex Federspiel
Problems 22
- A triangle has side lengths 131313, 141414, and xxx. How many possible integer values of xxx are there?
- Circle S1S_1S1 has radius 555. Circle S2S_2S2 has radius 777 and has its center lying on S1S_1S1. Circle S3S_3S3 has an integer radius and has its center lying on S2S_2S2. …
- Which point on the circle (x−11)2+(y−13)2=116(x - 11)^2 + (y - 13)^2 = 116(x−11)2+(y−13)2=116 is farthest from the point (41,25)(41, 25)(41,25)? Source: Math Prize for Girls
- For what kind of triangles does the triangle inequality hold true for?
- Can a triangle with the following side lengths exist? 2.5,2,32.5, 2, 32.5,2,3
- Can a triangle with the following side lengths exist? 1,4,41, 4, 41,4,4
- Can a triangle with the following side lengths exist? 0,4,40, 4, 40,4,4
- Can a triangle with the following side lengths exist? 9,3,49, 3, 49,3,4
- Can a triangle with the following side lengths exist? 9,3,x9, 3, x9,3,x
- If Tom lives 333 miles away from Julia, and Julia lives 777 miles away from Mitch, what is the maximum distance Tom can live from Mitch?
- If Tom lives 333 miles away from Julia, and Julia lives 777 miles away from Mitch, what is the minimum distance Tom can live from Mitch?
- If Tariq lives 666 miles away from James, and James lives 777 miles away from Miriam, what is the minimum distance Tariq can live from Miriam?
- If Tariq lives 666 miles away from James, and James lives 777 miles away from Miriam, what is the maximum distance Tariq can live from Miriam?
- You have traveled west on the Oregon Trail, survived dysentery, and have staked your claim on a new plot of land. You have 4 miles of fence which you can put in any shape you'd …
- A bakery sells unusually sized loaves of bread. One day, 3 baguettes fell on the ground; they measured exactly 8 cm, 17 cm, and 26 cm. How many possible unique triangles could t…
- If an isosceles triangle has a perimeter of 40 units, what is the number of possible combinations for the base (unique) side of the triangle, assuming all sides have length that…
- What do you think? Should the police question the suspect any further?
- A triangle with integer side lengths has one side that is six times the length of the second side and a third side of length 707070. What is the difference between largest and s…
- A triangle has side lengths 222222, 333333, and xxx, where xxx is an integer. How many possible values of xxx are there?
- A triangle has side lengths log2\log 2log2, log4\log 4log4, and logx\log xlogx, where xxx is an integer. How many possible values of xxx are there?
- Two sides of a triangle have lengths 444 and 14.14.14. What is the range of possible values of the semiperimeter of the triangle?
- A triangle's longest side has length 15,15,15, and the difference in lengths of the other two sides is at most 555. What is the smallest possible integer length of the shortest …