Question

The length of a golden rectangle is 8 cm. Find the width to the nearest tenth.

Answer 1

A golden rectangle is a rectangle with sides in golden ratio

`((a+b))/(b)=(b)/(a)`
`\begin{gathered} \text{where a}\Rightarrow is\text{ the width} \\ (a+b)\Rightarrow\text{ is the length} \end{gathered}`

From the question

`\begin{gathered} \text{lenght}=(a+b)=8 \\ a+b=8 \\ a=8-b \end{gathered}`

Substitute a in the golden ratio formula

`\begin{gathered} ((a+b))/(a)=(b)/(a) \\ Given\text{ that the ratio of the legth to the width is }1.618 \\ \text{Thus } \\ ((a+b))/(b)=1.618 \\ \text{ Since (a+b) = 8} \\ \text{Then} \\ (8)/(a)=1.618 \end{gathered}`

Cross multiply to find a (width)

Hence, the width of the golden rectangle to the nearest tenth is 4.9cm