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## OG 2020: Question No. 100

On a scale drawing, a rectangle 1 inch by 1(1/3) inches represents the floor of a room and the indicated scale is 1-inch equals 15 feet. How many square tiles 6 inches on a side will be needed to cover this floor? (1 foot = 12 inches)

1. 40
2. 70
3. 120
4. 700
5. 1,200
 Source OG 2020 Type Problem Solving Topic Geometry Sub-Topic Miscellaneous Difficulty Medium

### Solution

#### Given:

• Dimensions of the rectangular floor = 1 inch byĀ 1(1/3) inches
• 1 inch = 15 feet
• 1 feet = 12 inches

#### To find:

• The number of square tiles 6 inches on a side will be needed to cover this floor.

#### Approach and Working:

• Dimensions of the rectangle in feet= 1 * 15 feet by (4/3) * 15 feet = 15 feet by 20 Feet
• Dimensions of the rectangle in inches = 15 * 20 inches by 20 * 12 inches = 180 inches by 240 inches

Area of the floor = 180 * 240

• Total number of square tiles of side length 6 inches need to cover this floor = (180 * 240)/(6 * 6)Ā  = 1200

Hence, the correct answer is option E.

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