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Mathematics

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Zarrin [17]2 years ago

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A town is designing a rectangular park that will be 600 feet wide by 1000 feet long. On a scale drawing, the dimensions of the p

KonstantinChe [14]

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

$\rm 1\: ft : \dfrac{s}{k}\: in.$

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

$\rm 1\: ft : \dfrac{s}{k}\: in.$

Since it is given that 600 ft : 12 inches and 1000 ft : 20 inches, thus, we get:

$\rm 1\: ft : \dfrac{s}{k}\: in.\\\\600 \: ft = \dfrac{600\times s}{k} \: in. = 12 \: in.\\\\\dfrac{600 \times s}{k} = 12\\\\\dfrac{s}{k} = \dfrac{12}{600} = 0.02$

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:
$\rm L \times 0.02 = 0.5 \\\\L = \dfrac{0.5}{0.02} = 25 \:\\\\W \times 0.02 = 2 \\W = \dfrac{2}{0.02} = 100$