A rectangular park has a perimeter of and an area of

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

Problem

A rectangular park has a perimeter of

34\,\text{m}

and an area of

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

. Let the breadth of the park be

x\,\text{m}

and the length be

l\,\text{m}

. (i) Express

l

in terms of

x

using the perimeter condition. (ii) Form a quadratic equation in

x

using the area condition. (iii) Solve the quadratic equation to obtain possible values of

x

and hence of

l

. (iv) State the dimensions of the park, giving reasons for accepting or rejecting each value of

x

obtained.