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A scale drawing of a kitchen is shown below. The scale is 1 : 20. A rectangle is shown. The length of the rectangle is labeled 4 inches. The width of the rectangle is labeled 5 inches. Show your work to determine the area of the room in square feet.​

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55 $$\frac{5}{9}$$ feet² or 55.556 feet²

Step-by-step explanation:

The scale means that for ever one in the scale drawing, it is 20 in the actual room. We will convert the dimensions using proportions.

$$\frac{5}{x}=\frac{1}{20}$$

100 = x

-> The length is 100 inches

$$\frac{4}{x}=\frac{1}{20}$$

80 = x

-> The width is 80 inches

The area of a rectangle can be found by multiplying the length by the width:

A = L * W

A = 100 * 80

A = 8,000 inches²

To get this into square feet, we will divide by 144. Why? There are 12 inches in a foot. 12 times 12 is 144.

8,000 inches² / 144 = 55 $$\frac{5}{9}$$ feet²

The area of the room, in square feet, is 55 $$\frac{5}{9}$$ feet².
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