Mathematics

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}

. a. (i) Express

l

in terms of

x

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

x

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

x

and hence of

l

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

x

obtained.

Intuitive explanation

You have two constraints on a rectangle: its perimeter and area. The key is to set up two equations from these constraints, then use one to express length in terms of breadth (or vice versa), and substitute into the other to get a quadratic equation. Once you solve for the breadth, finding the length follows directly from either original equation.

Intuitive explanation

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