Question

problems 1 - 4: here is part of a scale drawing of zahras office. the scale is 6 centimeters to 15 feet. 1. what are the dimensions of the actual office? 2. what is the actual area of her office? 3. zahra 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. fabianas office is near zahras office and measures 4 centimeters by 8 centimeters in the scale drawing. is fabianas office twice the area of zahras 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 cm.

Step2: Find actual dimensions of Zahra's office

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

Step3: Find actual area of Zahra's office

Area = length $\times$ width, so $A = 5\times10 = 50$ square feet.

Step4: Find scale - drawing width of the couch

Let $x$ be the width on the scale - drawing. We know that $\frac{6}{15}=\frac{x}{3}$. Cross - multiply: $15x=6\times3$, so $x=\frac{6\times3}{15}=\frac{18}{15}=1.2$ cm.

Step5: Find actual dimensions of Fabiana's office

Length: $4\times\frac{5}{2}=10$ feet
Width: $8\times\frac{5}{2}=20$ feet
Area of Fabiana's office = $10\times20 = 200$ square feet.
Since $200\div50 = 4$, Fabiana's office is 4 times the area of Zahra's office, not 2 times.

Answer:

1. 5 feet by 10 feet
2. 50 square feet
3. 1.2 cm
4. No. The area of Zahra's office is 50 square feet and the area of Fabiana's office is 200 square feet. Fabiana's office is 4 times the area of Zahra's office, not 2 times.