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# The figure above represents a scale drawing of the floor of a room, an

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Math Expert
Joined: 02 Sep 2009
Posts: 47161
The figure above represents a scale drawing of the floor of a room, an  [#permalink]

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22 Sep 2017, 00:43
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79% (01:28) correct 21% (01:53) wrong based on 33 sessions

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The figure above represents a scale drawing of the floor of a room, and the drawing has the dimensions shown. If 1/4 inch on the drawing represents 1 foot, what is the area, in square feet, of the floor?

(A) 134
(B) 126
(C) 117
(D) 42
(E) 39

Attachment:

2017-09-22_1139.png [ 8.6 KiB | Viewed 713 times ]

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Re: The figure above represents a scale drawing of the floor of a room, an  [#permalink]

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22 Sep 2017, 01:33
Given 1/4 inch of drawing = 1 foot

Area of given figure = Area of 2 rectangles that can be formed
= 9/4* (15/4-3/4) +( 9/4-3/4) * 3/4
= 9/4inch * 12/4inch + 6/4 inch*3/4inch
= 9foot* 12 foot + 6foot*3 foot
= 126 sq foot

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The figure above represents a scale drawing of the floor of a room, an  [#permalink]

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22 Sep 2017, 18:35
Bunuel wrote:

The figure above represents a scale drawing of the floor of a room, and the drawing has the dimensions shown. If 1/4 inch on the drawing represents 1 foot, what is the area, in square feet, of the floor?

(A) 134
(B) 126
(C) 117
(D) 42
(E) 39

Attachment:
2017-09-22_1139.png

Convert each length to feet.* Multiply the whole base by the whole height of the rectangle, then subtract the area of the cut-out piece in the upper right corner.

$$\frac{1}{4}$$inch = $$1$$ foot, so
$$\frac{15}{4}in$$ = $$15$$ feet - Floor Length
$$\frac{9}{4}in$$ = $$9$$ feet - Floor Width
$$\frac{3}{4}in$$ = $$3$$ feet - Length of Cut-out sides

Find the area of a rectangle as if the corner had not been cut out. L * W = area
(15 * 9) = 135 sq ft

Find the area of the cut out corner:
(3 * 3) = 9 sq ft

Subtract the area of the cut out corner from the area of the rectangle to get area in square feet: 135 - 9 = 126

*There are a few ways to calculate conversion.

Denominator of 4 remains the same; I multiplied numerators (if 1 to 1, then 3 to 3, 15 to 15,etc.)

Cross multiplying is another way. Below, e.g., is conversion of $$\frac{15}{4}$$ inches to ___ feet

Where ratio is $$\frac{ScaleLenth}{ActualLenth}$$

$$\frac{\frac{1}{4}}{1}$$=$$\frac{\frac{15}{4}}{x}$$

$$\frac{1}{4}x = \frac{15}{4}$$

$$x = \frac{15}{4} * 4$$

$$x = 15$$

So $$\frac{15}{4}$$ inches = 15 feet
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Re: The figure above represents a scale drawing of the floor of a room, an  [#permalink]

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22 Sep 2017, 21:49

If 1/4 inch on the drawing represents 1 foot,
the fully formed rectangle will have dimensions 9 feet by 15 feet(with area : 135 feet)

The dimensions of the square will be 3 feet(with area : 9 feet)

Hence, the area of the figure must be 135-9 = 126 ft(Option B)

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Re: The figure above represents a scale drawing of the floor of a room, an &nbs [#permalink] 22 Sep 2017, 21:49
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