Solved on Dec 08, 2023

Find the area in square inches of a scale drawing of a classroom floor that is 34 ft long and 36 ft wide, if the scale drawing has a length of 17 inches.

STEP 1

Assumptions
1. The actual length of the classroom floor is 34 feet.
2. The actual width of the classroom floor is 36 feet.
3. The scale drawing length of the classroom floor is 17 inches.
4. The scale used for the drawing is consistent for both length and width.
5. The area of the floor in the scale drawing is required in square inches.

STEP 2

First, we need to determine the scale factor used for the drawing. We can do this by comparing the scale drawing length to the actual length.
Scalefactor=ScaledrawinglengthActuallengthScale\, factor = \frac{Scale\, drawing\, length}{Actual\, length}

STEP 3

Convert the actual length from feet to inches, since the scale drawing is measured in inches. There are 12 inches in a foot.
Actuallengthininches=Actuallengthinfeet×12Actual\, length\, in\, inches = Actual\, length\, in\, feet \times 12

STEP 4

Now, plug in the actual length in feet to find the actual length in inches.
Actuallengthininches=34feet×12inches/footActual\, length\, in\, inches = 34\, feet \times 12\, inches/foot

STEP 5

Calculate the actual length in inches.
Actuallengthininches=34×12=408inchesActual\, length\, in\, inches = 34 \times 12 = 408\, inches

STEP 6

Now, calculate the scale factor using the scale drawing length and the actual length in inches.
Scalefactor=17inches408inchesScale\, factor = \frac{17\, inches}{408\, inches}

STEP 7

Simplify the scale factor.
Scalefactor=124Scale\, factor = \frac{1}{24}

STEP 8

Next, we need to find the width of the classroom floor in the scale drawing using the same scale factor. First, convert the actual width from feet to inches.
Actualwidthininches=Actualwidthinfeet×12Actual\, width\, in\, inches = Actual\, width\, in\, feet \times 12

STEP 9

Now, plug in the actual width in feet to find the actual width in inches.
Actualwidthininches=36feet×12inches/footActual\, width\, in\, inches = 36\, feet \times 12\, inches/foot

STEP 10

Calculate the actual width in inches.
Actualwidthininches=36×12=432inchesActual\, width\, in\, inches = 36 \times 12 = 432\, inches

STEP 11

Now, use the scale factor to find the width of the classroom floor in the scale drawing.
Scaledrawingwidth=Actualwidthininches×ScalefactorScale\, drawing\, width = Actual\, width\, in\, inches \times Scale\, factor

STEP 12

Plug in the actual width in inches and the scale factor to calculate the scale drawing width.
Scaledrawingwidth=432inches×124Scale\, drawing\, width = 432\, inches \times \frac{1}{24}

STEP 13

Calculate the scale drawing width.
Scaledrawingwidth=43224=18inchesScale\, drawing\, width = \frac{432}{24} = 18\, inches

STEP 14

Now that we have both the length and width of the classroom floor in the scale drawing, we can calculate the area of the floor in the scale drawing.
Areaofscaledrawing=Scaledrawinglength×ScaledrawingwidthArea\, of\, scale\, drawing = Scale\, drawing\, length \times Scale\, drawing\, width

STEP 15

Plug in the values for the scale drawing length and width to calculate the area of the scale drawing.
Areaofscaledrawing=17inches×18inchesArea\, of\, scale\, drawing = 17\, inches \times 18\, inches

STEP 16

Calculate the area of the scale drawing.
Areaofscaledrawing=17×18=306squareinchesArea\, of\, scale\, drawing = 17 \times 18 = 306\, square\, inches
The area of the floor in the scale drawing is 306 square inches.

Was this helpful?
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ContactInfluencer programPolicyTerms
TwitterInstagramFacebookTikTokDiscord