- A3
- B8
- C5
- D4
Step-by-Step Solution
Third side must be greater than 9 − 6 = 3. The smallest whole number greater than 3 is 4 cm.
Answer: D) 4
Two sides of a triangle are 6 cm and 9 cm. What is the smallest whole-number length (in cm) the third side can be?
Class 7The Triangle and its PropertiesTriangles
Key idea: Triangle inequality
**The sum of any two sides of a triangle is greater than the third side.**
So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.
Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.
So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.
Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All The Triangle and its Properties practice questions
More Class 7 The Triangle and its Properties practice
Two sides of a triangle are 6 cm and 9 cm. What is the largest whole-number length (in…Which set of lengths can form a triangle?A ladder 13 m long rests against a wall with its foot 5 m from the wall. How high up the…In a triangle, the angles are 90°, 45°, and 45°. Which type of triangle is it by sides?In a triangle, the longest side is always opposite the: