Question

problems 1 - 4: here is part of a scale drawing of dr. flosss office. the scale is 6 centimeters to 15 feet. show all work for the problems below. 1) what are the dimensions of the actual office? 2) what is the actual area of the office? 3) dr. floss wants to put a couch in her office that is 3 feet wide. how wide would the couch be if it were drawn on the scale drawing? 4) dr. brushs office is near dr. flosss office and measures 4 centimeters by 8 centimeters in the scale drawing. a) what are the real - life dimensions of dr. brushs office? b) what is the area of dr. brushs office? c) is dr. brushs office twice the area of dr. flosss office? explain your thinking.

Explanation:

Step1: Find the conversion factor

The scale is 6 cm to 15 feet. So the conversion factor is $\frac{15}{6}=\frac{5}{2}$ feet per centimeter.

Step2: Find actual dimensions of Dr. Floss's office

The scale - drawing dimensions of Dr. Floss's office are 2 cm by 4 cm.
Length: $4\times\frac{5}{2}=10$ feet
Width: $2\times\frac{5}{2}=5$ feet

Step3: Find actual area of Dr. Floss's office

Area = length $\times$ width. So the area of Dr. Floss's office is $10\times5 = 50$ square feet.

Step4: Find scale - drawing width of the couch

If the actual width of the couch is 3 feet, and the conversion factor is $\frac{5}{2}$ feet per centimeter. Let the scale - drawing width be $x$ cm. Then $\frac{5}{2}x=3$, so $x = 3\times\frac{2}{5}=1.2$ cm.

Step5: Find real - life dimensions of Dr. Brush's office

The scale - drawing dimensions of Dr. Brush's office are 4 cm by 8 cm.
Length: $8\times\frac{5}{2}=20$ feet
Width: $4\times\frac{5}{2}=10$ feet

Step6: Find area of Dr. Brush's office

Area = length $\times$ width. So the area of Dr. Brush's office is $20\times10 = 200$ square feet.

Step7: Compare the areas

The area of Dr. Floss's office is 50 square feet and the area of Dr. Brush's office is 200 square feet. $200\div50 = 4$, so Dr. Brush's office is 4 times the area of Dr. Floss's office, not 2 times.

Answer:

1. The actual dimensions of Dr. Floss's office are 5 feet by 10 feet.
2. The actual area of Dr. Floss's office is 50 square feet.
3. The couch would be 1.2 cm wide on the scale drawing.

4.
a. The real - life dimensions of Dr. Brush's office are 10 feet by 20 feet.
b. The area of Dr. Brush's office is 200 square feet.
c. No, Dr. Brush's office is 4 times the area of Dr. Floss's office, not 2 times since the area of Dr. Floss's office is 50 square feet and the area of Dr. Brush's office is 200 square feet.