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: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 thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetz-----> the scale drawingx-----> the area of the playground in the scale drawingy----> 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]orDivide by 4 both numerator and denominator[tex]z=\frac{1}{0.75}\frac{cm}{m}[/tex]