3 Sides Given: Challenge & Extension
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on constructing triangles given three sides (SSS). Designed for GCSE Foundation students to deepen understanding and develop problem-solving skills.
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Full preview • 11 questions
3 Sides Given: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Practice Questions
Answer all questions. Show your working clearly in the grid spaces provided.
1.
Construct a triangle with sides of lengths 5 cm, 7 cm, and 8 cm. Use the grid to accurately draw the triangle.
[4 marks]2.
Calculate the area of a triangle with sides 6 cm, 8 cm, and 10 cm using Heron's formula.
[3 marks]3.
Given a triangle with sides 9 cm, 12 cm, and 15 cm, determine whether the triangle is right-angled.
[2 marks]4.
Construct a triangle with sides of 4 cm, 6 cm, and 9 cm. Explain whether such a triangle can exist and justify your answer.
[4 marks]5.
If two sides of a triangle are 7 cm and 10 cm, what is the possible range for the third side?
[3 marks]6.
A triangle has sides of lengths 8 cm, 15 cm, and 22 cm. Is this triangle valid? Show your reasoning.
[4 marks]7.
Construct a triangle with sides 5 cm, 9 cm, and 12 cm. Use the grid to verify the triangle's existence and angles.
[4 marks]8.
A triangle has sides of 10 cm, 14 cm, and 9 cm. Calculate the exact length of the median from the vertex opposite the side of 14 cm.
[4 marks]9.
Identify a common mistake when constructing a triangle with sides 7 cm, 10 cm, and 22 cm and explain how to correct it.
[3 marks]10.
Challenge: Construct a triangle where the sides are in the ratio 3:4:5, with the shortest side measuring 6 cm. Confirm whether the triangle is right-angled.
[4 marks]11.
Prove that a triangle with sides 13 cm, 14 cm, and 25 cm cannot exist. Use the triangle inequality theorem to justify your answer.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet