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QuestionFind the perimeter, in inches, of a scale drawing of a classroom floor that is 30 ft long and 24 ft wide, with a 15 in length.

Studdy Solution

STEP 1

Assumptions1. The length of the actual floor is30 feet. The width of the actual floor is24 feet3. The length of the scale drawing is15 inches4. The scale is linear, meaning the same scale applies to both length and width5. The scale is consistent, meaning the same scale applies to the perimeter as well

STEP 2

First, we need to find the scale of the drawing. We can do this by dividing the length of the scale drawing by the length of the actual floor.
Scale=Length of scale drawingLength of actual floorScale = \frac{Length\, of\, scale\, drawing}{Length\, of\, actual\, floor}

STEP 3

Now, plug in the given values for the length of the scale drawing and the length of the actual floor to calculate the scale.
Scale=15 inches30 feetScale = \frac{15\, inches}{30\, feet}

STEP 4

As the measurements are in different units (inches and feet), we need to convert them to the same unit. We know that1 foot equals12 inches.
30 feet=30×12 inches30\, feet =30 \times12\, inches

STEP 5

Calculate the length of the actual floor in inches.
30 feet=30×12 inches=360 inches30\, feet =30 \times12\, inches =360\, inches

STEP 6

Now, we can calculate the scale using the same units (inches).
Scale=15 inches360 inchesScale = \frac{15\, inches}{360\, inches}

STEP 7

Calculate the scale.
Scale=15360=0.04167Scale = \frac{15}{360} =0.04167

STEP 8

Now that we have the scale, we can find the width of the scale drawing. This can be done by multiplying the width of the actual floor (in inches) by the scale.
Width of scale drawing=Width of actual floor×ScaleWidth\, of\, scale\, drawing = Width\, of\, actual\, floor \times Scale

STEP 9

Convert the width of the actual floor to inches.
24 feet=24×12 inches24\, feet =24 \times12\, inches

STEP 10

Calculate the width of the actual floor in inches.
24 feet=24×12 inches=288 inches24\, feet =24 \times12\, inches =288\, inches

STEP 11

Now, plug in the values for the width of the actual floor and the scale to calculate the width of the scale drawing.
Width of scale drawing=288 inches×0.04167Width\, of\, scale\, drawing =288\, inches \times0.04167

STEP 12

Calculate the width of the scale drawing.
Width of scale drawing=288×0.04167=12 inchesWidth\, of\, scale\, drawing =288 \times0.04167 =12\, inches

STEP 13

Now that we have the length and width of the scale drawing, we can calculate the perimeter. The perimeter of a rectangle is given by the formulaPerimeter=2×(Length+Width)Perimeter =2 \times (Length + Width)

STEP 14

Plug in the values for the length and width of the scale drawing to calculate the perimeter.
Perimeter=2×( inches+12 inches)Perimeter =2 \times (\, inches +12\, inches)

STEP 15

Calculate the perimeter of the scale drawing.
Perimeter=2×(15+12)=2×27=54 inchesPerimeter =2 \times (15 +12) =2 \times27 =54\, inchesThe perimeter of the floor in the scale drawing is54 inches.

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