Bunuel
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
ANSWER B*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