GB-19-05-001 · Quadratic modelling

A rectangle has area 672 cm². Its length is 4 cm more than its width. Work out the width.

Solving Quadratics by Factorising (Area Model) Booklet p. 12

Method

1) Form equation x(x + d) = Area and rearrange = 0

2) Factorise into double brackets

3) Solve and reject negative length

Worked Example (GB-19-05-001)

Let the width be x, so

x(x+4)=672\Rightarrow x^2+4x-672=0

Multiply

a\times c=1\times(-672)=-672

. Choose the signed factor pair

-24,\ 28

: product

-672

, sum

4

×	$x$	$-24$
$x$	$x^2$	$-24x$
$28$	$28x$	$-672$

Read the factors outside the grid:

(x + 28)(x - 24)

x + 28=0\quad\Rightarrow\quad x=-28

x - 24=0\quad\Rightarrow\quad x=24

Reject the negative root because a length is positive. Width

x=24

cm.

Ans = 24 cm