A square park has side length metres.

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

A square park has side length 103\dfrac{10}{\sqrt{3}} metres. (i) Find the exact area of the park in m2\text{m}^2, expressing your answer so that no irrational number remains in the denominator. (ii) A uniform path of width 23\dfrac{2}{\sqrt{3}} metres is to be laid all around the park. Calculate the exact area of the path alone, again ensuring that your final answer contains no irrational denominator.

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