Respuesta :
Answer:
The scale of the drawing is
[tex]\frac{4}{3}\frac{cm}{m}[/tex] or [tex]\frac{1}{0.75}\frac{cm}{m}[/tex]
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
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=16*8=128\ cm^{2}[/tex]
[tex]y=72\ m^{2}[/tex]
substitute
[tex]z^{2}=\frac{128}{72}[/tex]
simplify
[tex]z^{2}=\frac{16}{9}[/tex]
[tex]z=\frac{4}{3}\frac{cm}{m}[/tex]
or
Divide by 4 both numerator and denominator
[tex]z=\frac{1}{0.75}\frac{cm}{m}[/tex]
The scale of the drawing is 1 cm to 75 cm OR 1 cm to 0.75 m
Calculating the scale of a drawing
From the question, we are to determine the scale of the drawing
First, we will calculate the area of the playground on the scale drawing
Length of playground = 16 cm
Width of playground = 8 cm
Then,
Area of playground on the scale drawing = 16 cm × 8 cm
Area of playground on the scale drawing = 128 cm²
From the given information,
Area of the actual play ground = 72 m² = 720000 cm²
By similarity,
[tex]\frac{(Length\ of\ scale\ drawing)^{2} }{(Actual\ length)^{2} } = \frac{Area\ of \ scale \ drawing}{Actual \ area}[/tex]
Let the actual length of the playground be x
[tex]\frac{16^{2} }{x^{2} } = \frac{128}{720000}[/tex]
[tex]x^{2} =\frac{16^{2} \times 720000 }{128}[/tex]
[tex]x^{2} =\frac{256 \times 720000 }{128}[/tex]
[tex]x = 1200 \ cm[/tex]
Thus,
Actual length of the play ground = 1200 cm
Therefore,
Scale of the drawing = [tex]\frac{Length\ of\ the\ playground\ in\ the\ scale\ drawing}{Actual\ length}[/tex]
Scale of the drawing = [tex]\frac{16 \ cm}{ 1200 \ cm}[/tex]
Scale of the drawing = 1cm to 75cm OR 1cm to 0.75 m
Hence, the scale of the drawing is 1 cm to 75 cm OR 1 cm to 0.75 m
Learn more on Calculating the scale of a drawing here: https://brainly.com/question/22298974
