Geometry and TrigonometryHardLeast possible perimeter with an integer side
Geometry and Trigonometry practice question
Two sides of a triangle have lengths 4 and 9. If the third side has an integer length, what is the least possible perimeter of the triangle?
Answer: 19
The third side must be greater than 9 − 4 = 5 and less than 9 + 4 = 13. The smallest integer greater than 5 is 6. Perimeter: 4 + 9 + 6 = 19.
Common wrong answers
- If you answered 6
- 6 is the least possible third side, not the perimeter. Add the other two sides.
- If you answered 18
- 18 uses a third side of 5, but 4 + 5 = 9 is not GREATER than 9; the sides would lie flat. The third side must exceed 5.
- If you answered 25
- 25 uses the GREATEST integer third side, 12. The question asks for the least perimeter.
More Geometry and Trigonometry questions
- Hard
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg? - Hard
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Hard
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
What is 135° expressed in radians? - Hard
What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector?
Not affiliated with the College Board. SAT is a trademark of the College Board.