A rectangular garden has its length greater than twice its breadth

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

A rectangular garden has its length

1\,\text{m}

greater than twice its breadth. When each dimension is decreased by

3\,\text{m}

, the area reduces to

84\,\text{m}^{2}

. (i) Taking the breadth of the garden to be

x\,\text{m}

, set up a quadratic equation in

x

that models the given information. (ii) Factorise the quadratic equation obtained in part (i) and find all possible values of

x

. (iii) Hence determine the original dimensions of the garden.