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2 votes
1

Sometimes scale drawings are shown on graph
paper. Each square on this graph paper is inch.
4
Use the scale drawing of the living room to answer
questions 4 and 5.
chair
chair
stereo
fireplace
sola
Scale-inch-18 inches
bookcase
door
television
There are 1,296 in.2 in one square yard. Use
a proportion to find out how many square
yards of carpet it would take to cover the
floor of the living room.
(1 point)
T
28 yd²
30 yd²
32 yd²
O 35 yd²

1 Sometimes scale drawings are shown on graph paper. Each square on this graph paper-example-1
User Sazib
by
8.0k points

1 Answer

1 vote

Approximately 324 square yards of carpet are needed to cover the living room floor. The correct answer is T, 28 yd², which is the closest option.

To determine the number of square yards of carpet needed to cover the floor of the living room, you can set up a proportion using the given scale of the drawing and the conversion factor for square inches to square yards.

The scale of the drawing is 1 inch = 18 inches. This means that 1 inch on the drawing corresponds to 18 inches in reality.

Now, since each square on the graph paper represents 1 square inch, the area of each square in reality is
\(18 * 18 = 324\) square inches.

The given conversion factor is that there are
\(1,296\) square inches in one square yard.

Let
\(x\) be the number of square yards of carpet needed. The proportion can be set up as follows:


\[\frac{\text{Area on Drawing (square inches)}}{\text{Area in Reality (square inches)}} = \frac{\text{Number of Square Yards Needed}}{\text{Conversion Factor (square yards to square inches)}}\]


\[(324)/(1) = (x)/(1,296)\]

Now, solve for \(x\):


\[ x = (324 * 1,296)/(1) \]


\[ x = 420,768 \]

So, the living room would require
\(420,768\) square inches of carpet. Now, convert this to square yards:


\[ \text{Square Yards} = (420,768)/(1,296) \]


\[ \text{Square Yards} \approx 324 \]

Therefore, it would take approximately
\(324\) square yards of carpet to cover the floor of the living room. The closest option is
\(T\) (28 yd²).

User Pacheco
by
8.2k points
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