Ravi has four sticks of lengths 3 cm, 5 cm, 7 cm and 9 cm, drawn to scale. He picks any three of them to make a triangle. Which three sticks can NOT make a triangle?
Class 7The Triangle and its PropertiesTriangles
A3 cm, 5 cm and 9 cm
B3 cm, 5 cm and 7 cm
C5 cm, 7 cm and 9 cm
D3 cm, 7 cm and 9 cm
Step-by-Step Solution
The two shorter sides must add up to more than the longest side. For 3, 5, 9: 3+5=8<9, so no triangle. The others work: 3+5>7,5+7>9,3+7>9.
Answer: A) 3 cm, 5 cm and 9 cm
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.
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