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MatroZZZ [7]
3 years ago
14

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?
Mathematics
1 answer:
olga nikolaevna [1]3 years ago
5 0

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}

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Step-by-step explanation:

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Step-by-step explanation:

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