Question

A scale drawing of a rectangular desktop is 4 cm long (l) and 1.5 cm wide (w). The actual desktop is 1.2 m wide. What is the area of the actual desktop?

Answer 1

Given:

The length of the rectangular desktop in scale drawing, l=4 cm.

The width of the rectangular desktop in scale drawing, w=1.5 cm.

The width of the actual desktop, W=1.2 m.

The scale factor for obatining the original dimensions of the desktop is,

$S=\frac{W}{w}=\frac{1.2\text{ m}}{1.5\operatorname{cm}}=\frac{1.2\times10^2\text{ cm}}{1.5\text{cm}}=\frac{4\times10^2}{5}=80$

Multiply the length l of the rectangular desktop in scale drawing by the scale factor S to get the length of the actual desktop.

$\begin{gathered} L=l\times S \\ =4\text{ cm}\times80 \\ =4\times10^{-2}\text{ cm}\times\frac{1\text{ m}}{1\text{ cm}}\times80 \\ =\text{ 3.2m} \end{gathered}$

Now, the actual area of the desktop is,

$\begin{gathered} A=3.2m\times1.2\text{ m} \\ =3.84\text{ }m^2 \end{gathered}$

Therefore, the actual area of the desktop is 3.84 sq m.