The rectangular floor of a classroom is 32 feet in length and 26 feet in width. A scale drawing of the floor has a length of 16 inches. What is the perimeter, in inches, of the floor in the scale drawing?Answer: □ in.
Q. The rectangular floor of a classroom is 32 feet in length and 26 feet in width. A scale drawing of the floor has a length of 16 inches. What is the perimeter, in inches, of the floor in the scale drawing?Answer: □ in.
Identify dimensions and scale: Identify the actual dimensions of the classroom floor and the scale used in the drawing.The actual length of the classroom floor is 32 feet, and the actual width is 26 feet. The scale drawing has a length of 16 inches. We need to find the scale factor to use it for finding the width in the scale drawing and then calculate the perimeter.
Calculate scale factor: Calculate the scale factor.The scale factor is the ratio of the length in the scale drawing to the actual length. Since 1 foot is equal to 12 inches, we first convert the actual length from feet to inches: 32 feet ×12 inches/foot =384 inches. Now we can find the scale factor: Scale factor =actual length in incheslength in scale drawing=384 inches16 inches.
Simplify scale factor: Simplify the scale factor. Simplify the scale factor by dividing both the numerator and the denominator by the greatest common divisor, which is 16 in this case: Scale factor = 384 inches16 inches=241.
Calculate width in drawing: Calculate the width in the scale drawing using the scale factor.Now we use the scale factor to find the width in the scale drawing. First, convert the actual width from feet to inches: 26 feet×12 inches/foot=312 inches. Then multiply the actual width in inches by the scale factor: Width in scale drawing = 312 inches×(1/24).
Simplify width calculation: Simplify the calculation to find the width in the scale drawing. Width in scale drawing = 312 inches×(241)=13 inches.
Calculate perimeter: Calculate the perimeter of the scale drawing.The perimeter of a rectangle is the sum of all its sides. In the scale drawing, the length is 16 inches, and the width is 13 inches. So, the perimeter is 2 times the sum of the length and width: Perimeter = 2×(length+width)=2×(16 inches+13 inches).
Simplify perimeter calculation: Simplify the calculation to find the perimeter of the scale drawing.Perimeter = 2×(16 inches+13 inches)=2×29 inches=58 inches.