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The rectangular floor of a classroom is 36 feet in length and 39 feet in width. A scale drawing of the floor has a length of 12 inches. What is the area, in square inches, of the floor in the scale drawing?
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The rectangular floor of a classroom is 3636 feet in length and 3939 feet in width. A scale drawing of the floor has a length of 1212 inches. What is the area, in square inches, of the floor in the scale drawing?\newlineAnswer: \square in.2^{2}

Full solution

Q. The rectangular floor of a classroom is 3636 feet in length and 3939 feet in width. A scale drawing of the floor has a length of 1212 inches. What is the area, in square inches, of the floor in the scale drawing?\newlineAnswer: \square in.2^{2}
  1. Convert to inches: Convert the actual length of the classroom floor from feet to inches to match the units of the scale drawing.\newlineSince 11 foot equals 1212 inches, we multiply the length in feet by 1212 to get the length in inches.\newline3636 feet ×12\times 12 inches/foot = 432432 inches
  2. Determine scale factor: Determine the scale factor between the actual floor and the scale drawing.\newlineThe actual length is 432432 inches and the scale drawing length is 1212 inches.\newlineScale factor =Scale drawing lengthActual length= \frac{\text{Scale drawing length}}{\text{Actual length}}\newlineScale factor =12 inches432 inches= \frac{12 \text{ inches}}{432 \text{ inches}}\newlineScale factor =136= \frac{1}{36}
  3. Convert width to inches: Convert the actual width of the classroom floor from feet to inches.\newlineSince 11 foot equals 1212 inches, we multiply the width in feet by 1212 to get the width in inches.\newline3939 feet ×12\times 12 inches/foot =468= 468 inches
  4. Calculate width in drawing: Calculate the width of the classroom floor in the scale drawing using the scale factor.\newlineScale drawing width = Actual width ×\times Scale factor\newlineScale drawing width = 468468 inches ×\times 136\frac{1}{36}\newlineScale drawing width = 1313 inches
  5. Calculate area of drawing: Calculate the area of the scale drawing.\newlineArea = Length ×\times Width\newlineArea = 1212 inches ×\times 1313 inches\newlineArea = 156156 square inches

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