- ABetween 18 cm and 36 cm
- BBetween 22 cm and 36 cm
- CBetween 4 cm and 18 cm
- DBetween 22 cm and 40 cm
Step-by-Step Solution
The third side must satisfy 11 − 7 < x < 11 + 7, that is 4 < x < 18. The perimeter is 7+11+x=18+x, so it lies between 18 + 4 = 22 cm and 18 + 18 = 36 cm. Trap: quoting 4 cm to 18 cm, which is the range of the THIRD SIDE and not of the perimeter — the two known sides still have to be added back on.
Answer: B) Between 22 cm and 36 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.