Scale drawing takes scaled versions of original lengths. The actual length of the swing set area of the park is 25 ft long and 100 ft wide
<h3>How are scale drawings formed?</h3>
For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
![\rm 1\: ft : \dfrac{s}{k}\: in.](https://tex.z-dn.net/?f=%5Crm%201%5C%3A%20%20ft%20%3A%20%5Cdfrac%7Bs%7D%7Bk%7D%5C%3A%20%20in.)
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
For the given case, it is given that
Real dimension of a rectangular park : 600 ft by 1000 ft
In drawing, it was of 12 inches by 20 inches.
Let the scale that the drawing is using be k feet to s inches, then
![\rm 1\: ft : \dfrac{s}{k}\: in.](https://tex.z-dn.net/?f=%5Crm%201%5C%3A%20%20ft%20%3A%20%5Cdfrac%7Bs%7D%7Bk%7D%5C%3A%20%20in.)
Since it is given that 600 ft : 12 inches and 1000 ft : 20 inches, thus, we get:
![\rm 1\: ft : \dfrac{s}{k}\: in.\\\\600 \: ft = \dfrac{600\times s}{k} \: in. = 12 \: in.\\\\\dfrac{600 \times s}{k} = 12\\\\\dfrac{s}{k} = \dfrac{12}{600} = 0.02](https://tex.z-dn.net/?f=%5Crm%201%5C%3A%20%20ft%20%3A%20%5Cdfrac%7Bs%7D%7Bk%7D%5C%3A%20%20in.%5C%5C%5C%5C600%20%5C%3A%20ft%20%3D%20%5Cdfrac%7B600%5Ctimes%20s%7D%7Bk%7D%20%5C%3A%20in.%20%3D%20%2012%20%5C%3A%20in.%5C%5C%5C%5C%5Cdfrac%7B600%20%5Ctimes%20s%7D%7Bk%7D%20%3D%2012%5C%5C%5C%5C%5Cdfrac%7Bs%7D%7Bk%7D%20%3D%20%5Cdfrac%7B12%7D%7B600%7D%20%3D%200.02)
Thus, every feet is reduced 0.02 times in drawing.
Now,
it is given that in drawing, the rectangular area for swing sets is 0.5 inch to 2 inch.
Let its real length was L and real width was W. Then we have:
![\rm L \times 0.02 = 0.5 \\\\L = \dfrac{0.5}{0.02} = 25 \:\\\\W \times 0.02 = 2 \\W = \dfrac{2}{0.02} = 100](https://tex.z-dn.net/?f=%5Crm%20L%20%5Ctimes%200.02%20%3D%200.5%20%5C%5C%5C%5CL%20%3D%20%5Cdfrac%7B0.5%7D%7B0.02%7D%20%3D%2025%20%5C%3A%5C%5C%5C%5CW%20%5Ctimes%200.02%20%3D%202%20%5C%5CW%20%3D%20%5Cdfrac%7B2%7D%7B0.02%7D%20%3D%20100)
Since these are only magnitudes, and unit was converted from feet to inches, so we have L = 25 feet and W = 100 feet
Thus,
The actual length of the swing set area of the park is 25 ft long and 100 ft wide
Learn more about scaling here:
brainly.com/question/8765466