AQA · Mathematics · 8300
GCSE Maths: Triangles: lengths of sides
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Triangles: lengths of sides (Corbettmaths Video 327), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the triangle inequality theorem?
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The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
If two sides of a triangle are 10 cm and 14 cm, what is the maximum possible length the third side can approach (but not equal)?
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24 cm. The sum of the two shorter sides (10 + 14 = 24) gives the upper bound, which the third side must be less than.
If two sides of a triangle are 10 cm and 14 cm, what is the minimum possible length the third side can approach (but not equal)?
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4 cm. The absolute difference of the two sides (14 - 10 = 4) gives the lower bound, which the third side must be greater than.
For a triangle with sides 7.5 cm and 8.1 cm, why could 0.5 cm NOT be the length of the third side?
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Because 0.5 + 7.5 = 8 cm, which is less than 8.1 cm. The sum of any two sides must be greater than the third side.
If two sides of a triangle are 30 cm and 18 cm, what inequality must the third side y satisfy?
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12 < y < 48. The third side must be greater than the difference (30 - 18 = 12) and less than the sum (30 + 18 = 48) of the other two sides.
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