Mathematics

Mathematics

Problem

A rectangle has length 8 cm8\,\text{cm} and breadth 53−5 cm.\dfrac{5}{3-\sqrt{5}}\,\text{cm}. (i) Express the breadth in simplest form by rationalising the denominator. (ii) Hence calculate the area of the rectangle and write your answer in simplest radical form. (iii) If the area can be written as p+q5p+q\sqrt{5}, where pp and qq are rational numbers, find the values of pp and qq.

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