Parallel lines, quadrilaterals and triangles · Usually met around P3
Three sides of a triangle
The two shortest together must beat the longest.
How to do it
Method
The two shortest together must beat the longest
3 + 4 = 7 > 6
Another way
Between difference and sum
4 − 3 = 1, 4 + 3 = 7 → 2 to 6
In full
Three sticks make a triangle only if any two of them together are longer than the third. The quick check is the two shortest: if together they are longer than the longest, it works. 3, 4, 6: 3 + 4 = 7 and 7 > 6, yes. 3, 4, 8: 7 < 8, no. 3, 4, 7: 7 = 7, also no — the sticks would lie flat in a line. With two sides known, the third must be longer than their difference and shorter than their sum: with 3 and 4 it is more than 1 and less than 7, so in whole numbers 2 to 6.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Two sticks are 12 cm and 13 cm. To make a triangle, what is the longest the third stick can be, in whole centimetres?
Show the answer and working
Answer: 24 cm
It must be shorter than 12 + 13 = 25: at most 24 cm.
Example 2
Two sticks are 8 cm and 2 cm. To make a triangle, what is the shortest the third stick can be, in whole centimetres?
Show the answer and working
Answer: 7 cm
It must be longer than the difference, 6: at least 7 cm.
Example 3
Which set of sticks can make a triangle?
- A. 3, 2, 5 cm
- B. 4, 4, 7 cm
- C. 7, 6, 14 cm
- D. 5, 7, 14 cm
Choose the right answer
Show the answer and working
Answer: B. 4, 4, 7 cm
4 + 4 is longer than 7: only in this set do the two shortest beat the longest.
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