AQA · Mathematics · 8300
GCSE Maths: Pythagoras: rectangles/isosceles tri
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Pythagoras: rectangles/isosceles tri (Corbettmaths Video 260), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is Pythagoras' theorem used to calculate in a right-angled triangle?
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The length of an unknown side when the other two sides are known.
A 4 metre ladder is placed against a vertical wall with its base 1.5 metres from the wall. How far up the wall does it reach?
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Use Pythagoras: √(4² - 1.5²) = √(16 - 2.25) = √13.75 ≈ 3.71 metres.
How do you find the diagonal of a rectangle with length 20cm and width 8cm?
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Use Pythagoras: √(20² + 8²) = √(400 + 64) = √464 ≈ 21.5 cm.
How do you find the height of an isosceles triangle with equal sides 8cm and base 5cm?
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The height bisects the base, creating a right triangle. Use Pythagoras: h = √(8² - 2.5²) = √(64 - 6.25) = √57.75 ≈ 7.6 cm.
How can you verify whether a triangle is right-angled using side lengths?
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Check if a² + b² = c², where c is the longest side. If true, the triangle is right-angled.
Is a triangle with sides 4cm, 6cm, and 7cm a right-angled triangle?
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No. Check: 4² + 6² = 16 + 36 = 52, but 7² = 49. Since 52 ≠ 49, it is not right-angled.
A tree is 18m horizontally from a point and 20m diagonally from the same point. What is the tree's height?
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Use Pythagoras: h = √(20² - 18²) = √(400 - 324) = √76 ≈ 8.7 metres.
In an isosceles triangle, why does the perpendicular height from the apex bisect the base?
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Because the two equal sides create mirror symmetry, so the perpendicular from the apex divides the base into two equal parts.
When using Pythagoras' theorem, which side of a right-angled triangle is the hypotenuse?
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The longest side, opposite the right angle. It appears alone on one side of the equation c² = a² + b².
If a right triangle has one side 14cm and another 18cm, why are there two possible lengths for the third side?
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Because we don't know which is the hypotenuse. If 18cm is the hypotenuse: √(18² - 14²) ≈ 11.3cm. If the unknown is the hypotenuse: √(18² + 14²) ≈ 22.8cm.
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