A rectangle has length and breadth

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

A rectangle has length

8\,\text{cm}

and breadth

\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+q\sqrt{5}

, where

p

and

q

are rational numbers, find the values of

p

and

q

Related theory

Real Number System
Surds and rationalisation
Operations on real numbers
Number Systems

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