Shape and space · Ages 8–9

Three sides of a triangle worksheet

Part of: Parallel lines, quadrilaterals and triangles

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Shape and space · Ages 8–9

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Two sticks are 4 cm and 6 cm. To make a triangle, what is the shortest the third stick can be, in whole centimetres?
Answer:
2.Two sticks are 11 cm and 14 cm. To make a triangle, what is the longest the third stick can be, in whole centimetres?
Answer:
3.Two sticks are 5 cm and 2 cm. To make a triangle, what is the longest the third stick can be, in whole centimetres?
Answer:
4.Two sticks are 8 cm and 5 cm. To make a triangle, what is the shortest the third stick can be, in whole centimetres?
Answer:
5.Two sticks are 8 cm and 4 cm. To make a triangle, what is the shortest the third stick can be, in whole centimetres?
Answer:
6.Two sides are 2 cm and 8 cm and the third is a whole number of centimetres. The third side is at least cm and at most cm.
Fill in each blank
Answer:
7.Two sides are 9 cm and 3 cm and the third is a whole number of centimetres. The third side is at least cm and at most cm.
Fill in each blank
Answer:
8.Two sides are 11 cm and 14 cm and the third is a whole number of centimetres. The third side is at least cm and at most cm.
Fill in each blank
Answer:

13.May has bamboo sticks of 11 cm and 17 cm and wants a third to make a triangle. What is the shortest the third can be, in whole centimetres?
Working:
Answer:
14.Ka-yan has straws of 11 cm and 11 cm and wants to cut a third to make a triangle. What is the longest the third can be, in whole centimetres?
Working:
Answer:
15.A triangular flower bed has two sides of 4 m and 6 m, and the third is a whole number of metres. How many different lengths could the third side be?
Working:
Answer:
16.A triangular flower bed has two sides of 4 m and 9 m, and the third is a whole number of metres. How many different lengths could the third side be?
Working:
Answer:
17.Tsz-hin has straws of 16 cm and 15 cm and wants to cut a third to make a triangle. What is the longest the third can be, in whole centimetres?
Working:
Answer:
18.Ming has bamboo sticks of 14 cm and 20 cm and wants a third to make a triangle. What is the shortest the third can be, in whole centimetres?
Working:
Answer:

Show the answers and working

Three sides of a triangle worksheet: Answers and working

1. 3 cm
The third must be longer than the difference between 4 and 6. Work out that difference first.
It must be longer than the difference, 2: at least 3 cm.
2. 24 cm
The third must be shorter than 11 + 14. Work that out, then think of the biggest whole number below it.
It must be shorter than 11 + 14 = 25: at most 24 cm.
3. 6 cm
The third must be shorter than 5 + 2. Work that out, then think of the biggest whole number below it.
It must be shorter than 5 + 2 = 7: at most 6 cm.
4. 4 cm
The third must be longer than the difference between 8 and 5. Work out that difference first.
It must be longer than the difference, 3: at least 4 cm.
5. 5 cm
The third must be longer than the difference between 8 and 4. Work out that difference first.
It must be longer than the difference, 4: at least 5 cm.
6. 7, 9
The third side is longer than the difference of 2 and 8 and shorter than their sum. Work out both first.
Longer than the difference and shorter than the sum of 2 and 8: 7 to 9.
7. 7, 11
The third side is longer than the difference of 9 and 3 and shorter than their sum. Work out both first.
Longer than the difference and shorter than the sum of 9 and 3: 7 to 11.
8. 4, 24
The third side is longer than the difference of 11 and 14 and shorter than their sum. Work out both first.
Longer than the difference and shorter than the sum of 11 and 14: 4 to 24.

9. A. 4, 4, 4 cm
Check each set: do the two shorter sticks add up to more than the longest?
With three equal sticks any two together are longer than the third, so 4, 4 and 4 cm make a triangle.
10. True
Find the longest of 2, 4 and 4 first, then add the other two and compare with it.
Any two sticks together must be longer than the third. 2 + 4 and 4 + 4 both beat the stick left over, so it comes down to 2 + 4 = 6: it must be longer than 4.
11. True
Find the longest of 3, 10 and 9 first, then add the other two and compare with it.
Any two sticks together must be longer than the third. 3 + 10 and 9 + 10 both beat the stick left over, so it comes down to 3 + 9 = 12: it must be longer than 10.
12. A. 5, 7, 11 cm
Check each set: do the two shortest sticks add up to more than the longest?
5 + 7 is longer than 11: only in this set do the two shortest beat the longest.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7 cm
The two shorter sticks together must be longer than the longest. The third plus 11 cm must beat 17 cm.
The third and the 11 cm stick together must be longer than 17 cm, so the third must be longer than 17 − 11 = 6 cm: at least 7 cm.
14. 21 cm
The third must be shorter than the other two together. Work out 11 + 11 first.
Shorter than 11 + 11: at most 21 cm.
15. 7 lengths
The third side is longer than the difference of 4 and 6 and shorter than their sum. Work out both first.
Longer than the difference, shorter than the sum: count the whole numbers between, 7.
16. 7 lengths
The third side is longer than the difference of 4 and 9 and shorter than their sum. Work out both first.
Longer than the difference, shorter than the sum: count the whole numbers between, 7.
17. 30 cm
The third must be shorter than the other two together. Work out 16 + 15 first.
Shorter than 16 + 15: at most 30 cm.
18. 7 cm
The two shorter sticks together must be longer than the longest. The third plus 14 cm must beat 20 cm.
The third and the 14 cm stick together must be longer than 20 cm, so the third must be longer than 20 − 14 = 6 cm: at least 7 cm.

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