GCSE Maths Practice: pythagoras-theorem

Question 8 of 10

This question tests rearranging Pythagoras' Theorem to find a shorter side of a right-angled triangle.

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\( \begin{array}{l}\text{Which rearrangement finds a shorter side in a right-angled triangle?}\end{array} \)

Choose one option:

\( b = \sqrt{c^2 - a^2} \) \( b = c^2 + a^2 \) \( b = \sqrt{a^2 + c^2} \) \( b = \sqrt{c^2 \times a^2} \)

Subtract the square of the known side from the hypotenuse squared, then take the square root.

When one side and the hypotenuse are known in a right-angled triangle, the missing side can be found by rearranging Pythagoras' Theorem: b^2 = c^2 - a^2, then b = √(c^2 - a^2). This skill is essential for problem-solving in GCSE geometry, ensuring accurate calculations and logical reasoning when determining distances or sides. Practising this rearrangement develops algebraic manipulation skills and confidence in applying the theorem.