Question

The diagram shows a scale drawing of a playground. In the scale drawing the playground has a length of 16 cm and a width of 8 cm. The area of the actual playground is 72 square meters what is the scale of the drawing?

Answer 1

Answer:

The scale of the drawing is

$\frac{4}{3}\frac{cm}{m}$  or  $\frac{1}{0.75}\frac{cm}{m}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale drawing

x-----> the area of the playground in the scale drawing

y----> the area of the actual playground

$z^{2}=\frac{x}{y}$

we have

$x=16*8=128\ cm^{2}$

$y=72\ m^{2}$

substitute

$z^{2}=\frac{128}{72}$

simplify

$z^{2}=\frac{16}{9}$

$z=\frac{4}{3}\frac{cm}{m}$

or

Divide by 4 both numerator and denominator

$z=\frac{1}{0.75}\frac{cm}{m}$