A rectangular playground has an area of

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

384\,\text{m}^2

. The length of the playground exceeds its width by

8\,\text{m}

. For safety reasons, the width must not be more than

20\,\text{m}

. (i) If the width of the playground is taken as

x\,\text{m}

, write an equation in

x

that represents the given information. (ii) Solve the equation obtained in part (i) and write the two possible values of

x

obtained. (iii) Using the safety restriction, decide which value of

x

is acceptable. Hence find the dimensions of the playground.