A square park has an area of

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

A=\sqrt{1800}\,\text{m}^{2}

. The park is to be surrounded by a path of uniform width

2\sqrt{2}\,\text{m}

. Answer the following. (i) Simplify

A

and write the result in the form

p\sqrt{q}\,\text{m}^{2}

, where

p

and

q

are positive integers and

q

has no perfect square factor other than

1

. (ii) Determine the length of one side of the square park, expressing your answer in simplest radical form. (iii) Find, in simplest radical form, the area of the path that surrounds the park. (iv) Using

\sqrt{2}\approx1.414

, calculate the area of the path correct to one decimal place.

Related theory

Composite Solids
Real Number System
Surds and rationalisation

Browse the problem library